%0 Journal Article %J Journal of Functional Analysis %D 2016 %T Existence and non-existence results for the SU(3) singular Toda system on compact surfaces %A Luca Battaglia %A Andrea Malchiodi %K Liouville-type equations %K Min–max solutions %K Non-existence results %K Toda system %X

We consider the SU(3) singular Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑m=1Mα1m(δpm−1)−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑m=1Mα2m(δpm−1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>−1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities."

%B Journal of Functional Analysis %V 270 %P 3750 - 3807 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123615004942 %R https://doi.org/10.1016/j.jfa.2015.12.011 %0 Journal Article %J Annali della Scuola Normale Superiore di Pisa. Classe di scienze %D 2016 %T Symmetry properties of some solutions to some semilinear elliptic equations %A Farina, Alberto %A Andrea Malchiodi %A Matteo Rizzi %B Annali della Scuola Normale Superiore di Pisa. Classe di scienze %I Classe di Scienze %V 16 %P 1209–1234 %G eng %0 Journal Article %J Advances in Mathematics %D 2015 %T A general existence result for the Toda system on compact surfaces %A Luca Battaglia %A Aleks Jevnikar %A Andrea Malchiodi %A David Ruiz %K Geometric PDEs %K Min–max schemes %K Variational methods %X

In this paper we consider the following Toda system of equations on a compact surface:−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−Δu1=−4π∑j=1mα1,j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−Δu2=−4π∑j=1mα2,j(δpj−1), which is motivated by the study of models in non-abelian Chern–Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation−Δu=ρ1(heu∫ΣheudVg−1)−ρ2(he−u∫Σhe−udVg−1), which arises in fluid dynamics."

%B Advances in Mathematics %V 285 %P 937 - 979 %G eng %U http://www.sciencedirect.com/science/article/pii/S0001870815003072 %R https://doi.org/10.1016/j.aim.2015.07.036 %0 Journal Article %J Analysis & PDE %D 2015 %T A topological join construction and the Toda system on compact surfaces of arbitrary genus %A Aleks Jevnikar %A Kallel, Sadok %A Andrea Malchiodi %B Analysis & PDE %I Mathematical Sciences Publishers %V 8 %P 1963–2027 %G eng %R 10.2140/apde.2015.8.1963 %0 Journal Article %D 2014 %T Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription %A Rod R. Gover %A Yaiza Canzani %A Dmitry Jakobson %A Raphaël Ponge %A Andrea Malchiodi %X In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures. %I Oxford University Press %G en %U http://urania.sissa.it/xmlui/handle/1963/35128 %1 35366 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T16:09:57Z No. of bitstreams: 1 preprint2014.pdf: 356671 bytes, checksum: 20e817f9f20d9c72d717e04f94f86bd9 (MD5) %R 10.1093/imrn/rns295 %0 Journal Article %D 2014 %T Critical points of the Moser-Trudinger functional on a disk %A Andrea Malchiodi %A Luca Martinazzi %X On the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe. %I European Mathematical Society %G en %U http://hdl.handle.net/1963/6560 %1 6487 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:24:49Z No. of bitstreams: 1 1203.1077v1.pdf: 218315 bytes, checksum: 7e4a2900b082b373371033ed0196f5de (MD5) %R 10.4171/JEMS/450 %0 Journal Article %J Bull. Inst. Math. Acad. Sin. %D 2014 %T A Moser-Trudinger inequality for the singular Toda system %A Luca Battaglia %A Andrea Malchiodi %B Bull. Inst. Math. Acad. Sin. %V 9 %P 1–23 %G eng %0 Journal Article %J Communications in Mathematical Physics 322, nr.2 (2013): 415-452 %D 2013 %T An improved geometric inequality via vanishing moments, with applications to singular Liouville equations %A Mauro Bardelloni %A Andrea Malchiodi %B Communications in Mathematical Physics 322, nr.2 (2013): 415-452 %I SISSA %G en %U http://hdl.handle.net/1963/6561 %1 6486 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:23:46Z No. of bitstreams: 2 1206.0225v2.pdf: 376591 bytes, checksum: 84aab361b9f74c6f00164ed271fe2cfd (MD5) 1206.0225v2.pdf: 376591 bytes, checksum: 84aab361b9f74c6f00164ed271fe2cfd (MD5) %R 10.1007/s00220-013-1731-0 %0 Journal Article %J Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371 %D 2013 %T A variational Analysis of the Toda System on Compact Surfaces %A Andrea Malchiodi %A David Ruiz %X In this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2. %B Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371 %I Wiley %G en %U http://hdl.handle.net/1963/6558 %1 6489 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:26:34Z No. of bitstreams: 1 1105.3701v2.pdf: 306787 bytes, checksum: f64fe03fd72ea85831e8f8ca25e9f99e (MD5) %R 10.1002/cpa.21433 %0 Journal Article %J Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 %D 2012 %T A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group. %A Andrea Malchiodi %A Paul Yang %A Jih-Hsin Cheng %A JennFang Hwang %X In this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 1 %B Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 %I SISSA %G en %U http://hdl.handle.net/1963/6556 %1 6490 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-03-25T14:33:32Z (GMT) No. of bitstreams: 0 %R 10.1515/CRELLE.2011.159 %0 Journal Article %J Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37 %D 2012 %T Non-uniqueness results for critical metrics of regularized determinants in four dimensions %A Matthew Gursky %A Andrea Malchiodi %X The regularized determinant of the Paneitz operator arises in quantum gravity (see Connes 1994, IV.4.$\gamma$). An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in Branson (1996). A similar formula holds for Cheeger's half-torsion, which plays a role in self-dual field theory (see Juhl, 2009), and is defined in terms of regularized determinants of the Hodge laplacian on $p$-forms ($p < n/2$). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in Chang and Yang (1995), Branson, Chang, and Yang (1992), and Gursky (1997). We also study entire solutions of the Euler-Lagrange equation of $\log \det P$ and the half-torsion $\tau_h$ on $\mathbb{R}^4 \setminus {0}$, and show the existence of two families of periodic solutions. One of these families includes Delaunay-type solutions. %B Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37 %I Springer %G en %U http://hdl.handle.net/1963/6559 %1 6488 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:25:46Z No. of bitstreams: 1 1105.3762v3.pdf: 658857 bytes, checksum: 2821cb9caed2f5cda3b406c745b73009 (MD5) %R 10.1007/s00220-012-1535-7 %0 Journal Article %J Journal of Functional Analysis 262 (2012) 409-450 %D 2012 %T Weighted barycentric sets and singular Liouville equations on compact surfaces %A Alessandro Carlotto %A Andrea Malchiodi %X Given a closed two dimensional manifold, we prove a general existence result\\r\\nfor a class of elliptic PDEs with exponential nonlinearities and negative Dirac\\r\\ndeltas on the right-hand side, extending a theory recently obtained for the\\r\\nregular case. This is done by global methods: since the associated Euler\\r\\nfunctional is in general unbounded from below, we need to define a new model\\r\\nspace, generalizing the so-called space of formal barycenters and\\r\\ncharacterizing (up to homotopy equivalence) its very low sublevels. As a\\r\\nresult, the analytic problem is reduced to a topological one concerning the\\r\\ncontractibility of this model space. To this aim, we prove a new functional\\r\\ninequality in the spirit of [16] and then we employ a min-max scheme based on a cone-style construction, jointly with the blow-up analysis given in [5] (after\\r\\n[6] and [8]). This study is motivated by abelian Chern- Simons theory in\\r\\nself-dual regime, or from the problem of prescribing the Gaussian curvature in\\r\\npresence of conical singularities (hence generalizing a problem raised by\\r\\nKazdan and Warner in [26]). %B Journal of Functional Analysis 262 (2012) 409-450 %I Elsevier %G en %U http://hdl.handle.net/1963/5218 %1 5040 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-10T11:49:50Z\\nNo. of bitstreams: 1\\n1105.2363v2.pdf: 793763 bytes, checksum: 4996db876d03946c03fa0d4766801974 (MD5) %R 10.1016/j.jfa.2011.09.012 %0 Journal Article %J Proc. Amer. Math. Soc. 139 (2011), 1023-1032 %D 2011 %T Axial symmetry of some steady state solutions to nonlinear Schrödinger equations %A Changfeng Gui %A Andrea Malchiodi %A Haoyuan Xu %A Paul Yang %K Nonlinear Schrödinger equation %X In this note, we show the axial symmetry of steady state solutions of nonlinear Schrodinger equations when the exponent of the nonlinearity is between the critical Sobolev exponent of n dimensional space and n - 1 dimensional space. %B Proc. Amer. Math. Soc. 139 (2011), 1023-1032 %I American Mathematical Society %G en_US %U http://hdl.handle.net/1963/4100 %1 304 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-11-10T10:42:02Z\\r\\nNo. of bitstreams: 1\\r\\nGui_Malchiodi_75M.pdf: 196044 bytes, checksum: ed4d2f1be79209d4b3e7d428564d043a (MD5) %R 10.1090/S0002-9939-2010-10638-X %0 Journal Article %J Comptes Rendus Mathematique 349 (2011) 161-166 %D 2011 %T A class of existence results for the singular Liouville equation %A Alessandro Carlotto %A Andrea Malchiodi %X We consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional. %B Comptes Rendus Mathematique 349 (2011) 161-166 %I Elsevier %G en %U http://hdl.handle.net/1963/5793 %1 5648 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-05-07T07:37:16Z\\nNo. of bitstreams: 0 %R 10.1016/j.crma.2010.12.016 %0 Report %D 2011 %T Critical points of the Moser-Trudinger functional %A Francesca De Marchis %A Andrea Malchiodi %A Luca Martinazzi %K Moser-Trudinger inequality %I SISSA %G en %U http://hdl.handle.net/1963/4592 %1 4353 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-07T11:40:39Z\\nNo. of bitstreams: 1\\n46M_Malchiodi.pdf: 234581 bytes, checksum: 365098bf21692bfa547056b200acb4c6 (MD5) %0 Journal Article %J Geometric and Functional Analysis 21 (2011) 1196-1217 %D 2011 %T New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces %A Andrea Malchiodi %A David Ruiz %X We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results. %B Geometric and Functional Analysis 21 (2011) 1196-1217 %I Springer %G en_US %U http://hdl.handle.net/1963/4099 %1 305 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-11-10T10:27:54Z\\r\\nNo. of bitstreams: 1\\r\\nMalchiodi-Ruiz-74M.pdf: 192985 bytes, checksum: 61acb10ab3cde055824228920d16987a (MD5) %R 10.1007/s00039-011-0134-7 %0 Journal Article %J Int Math Res Notices (2011) 2011 (24): 5625-5643 %D 2011 %T Supercritical conformal metrics on surfaces with conical singularities %A Mauro Bardelloni %A Francesca De Marchis %A Andrea Malchiodi %X

We study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

%B Int Math Res Notices (2011) 2011 (24): 5625-5643 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/4095 %1 309 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-26T07:12:29Z\\r\\nNo. of bitstreams: 1\\r\\nBarDemMal-56M.pdf: 317906 bytes, checksum: 6b2dc3222c15d6690b75440300fa4aed (MD5) %R 10.1093/imrn/rnq285 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 %D 2010 %T Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions %A Jesus Garcia Azorero %A Andrea Malchiodi %A Luigi Montoro %A Ireneo Peral %X In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in. %B Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 %G en_US %U http://hdl.handle.net/1963/3409 %1 926 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-08T11:10:32Z\\nNo. of bitstreams: 1\\nGMMPII.pdf: 324708 bytes, checksum: 4829f5449fac58672d6e7a8e42efb3c4 (MD5) %R 10.1016/j.anihpc.2009.06.005 %0 Journal Article %J Arch. Ration. Mech. Anal. 196 (2010) 907-950 %D 2010 %T Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results %A Jesus Garcia Azorero %A Andrea Malchiodi %A Luigi Montoro %A Ireneo Peral %X In this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero. %B Arch. Ration. Mech. Anal. 196 (2010) 907-950 %G en_US %U http://hdl.handle.net/1963/3406 %1 927 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-08T11:03:36Z\\nNo. of bitstreams: 1\\nGMMPI.pdf: 466523 bytes, checksum: 004f66da4f9e531a535780337f19e185 (MD5) %R 10.1007/s00205-009-0259-0 %0 Journal Article %J Adv. Math. 221 (2009) 1843-1909 %D 2009 %T Some new entire solutions of semilinear elliptic equations on Rn %A Andrea Malchiodi %B Adv. Math. 221 (2009) 1843-1909 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3645 %1 659 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-08T15:11:59Z\\nNo. of bitstreams: 1\\nentire.pdf: 478191 bytes, checksum: 1b7ea59917a621bf7b2793f7228fade6 (MD5) %R 10.1016/j.aim.2009.03.012 %0 Journal Article %J Front. Math. China 3 (2008) 239-252 %D 2008 %T Concentrating solutions of some singularly perturbed elliptic equations %A Andrea Malchiodi %X We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry. %B Front. Math. China 3 (2008) 239-252 %G en_US %U http://hdl.handle.net/1963/2657 %1 1466 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-05-12T13:25:45Z\\nNo. of bitstreams: 1\\nprocmalchiodi.pdf: 183157 bytes, checksum: 5d6ee64d87eb139b09968558c74ab0f5 (MD5) %R 10.1007/s11464-008-0015-z %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72 %D 2008 %T Entire solutions of autonomous equations on Rn with nontrivial asymptotics %A Andrea Malchiodi %X We prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic. %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72 %G en_US %U http://hdl.handle.net/1963/2640 %1 1483 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-30T08:06:29Z\\nNo. of bitstreams: 1\\ngluingnote.pdf: 178833 bytes, checksum: eca0da57985e983d19aac5964c9a1e55 (MD5) %0 Journal Article %J Ann. of Math. 168 (2008) 813-858 %D 2008 %T Existence of conformal metrics with constant $Q$-curvature %A Zindine Djadli %A Andrea Malchiodi %X Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author. %B Ann. of Math. 168 (2008) 813-858 %G en_US %U http://hdl.handle.net/1963/2308 %1 1708 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:05:55Z\\nNo. of bitstreams: 1\\nDjadliMalchiodiFinal.pdf: 342979 bytes, checksum: fc2b0b8e4e01a5327ed8e01dc1bae6c5 (MD5) %0 Journal Article %J Adv. Differential Equations 13 (2008) 1109-1129 %D 2008 %T Morse theory and a scalar field equation on compact surfaces %A Andrea Malchiodi %B Adv. Differential Equations 13 (2008) 1109-1129 %I Khayyam Publishing %G en_US %U http://hdl.handle.net/1963/3531 %1 733 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-20T09:55:31Z\\nNo. of bitstreams: 1\\nMalchiodi07.pdf: 259636 bytes, checksum: f8380ae02625bce2ba51c6bf7dcb737d (MD5) %0 Journal Article %J Discrete Contin. Dyn. Syst. 21 (2008) 277-294 %D 2008 %T Topological methods for an elliptic equation with exponential nonlinearities %A Andrea Malchiodi %X We consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the Moser-Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a min-max argument to obtain existence results. %B Discrete Contin. Dyn. Syst. 21 (2008) 277-294 %G en_US %U http://hdl.handle.net/1963/2594 %1 1528 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-02-26T11:51:21Z\\nNo. of bitstreams: 1\\nnotemalchiodi.pdf: 260737 bytes, checksum: eddd4d053e3aa35b1cd0562f82bd0e7e (MD5) %R 10.3934/dcds.2008.21.277 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631 %D 2008 %T Transition layer for the heterogeneous Allen-Cahn equation %A Fethi Mahmoudi %A Andrea Malchiodi %A Juncheng Wei %X We consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$. %B Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631 %G en_US %U http://hdl.handle.net/1963/2656 %1 1467 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-05-12T13:00:33Z\\nNo. of bitstreams: 1\\n0702878v1.pdf: 345060 bytes, checksum: a1e9182e6448c835b1c66b4f226b0b8d (MD5) %R 10.1016/j.anihpc.2007.03.008 %0 Journal Article %J J. Fixed Point Theory Appl. 1 (2007) 305-336 %D 2007 %T Boundary interface for the Allen-Cahn equation %A Andrea Malchiodi %A Juncheng Wei %B J. Fixed Point Theory Appl. 1 (2007) 305-336 %G en_US %U http://hdl.handle.net/1963/2027 %1 2169 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T11:10:26Z\\nNo. of bitstreams: 1\\nMalchiodiWei07.pdf: 379788 bytes, checksum: 4c87f76e7db9858a9acfeca0a8ec75c1 (MD5) %R 10.1007/s11784-007-0016-7 %0 Journal Article %J Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 %D 2007 %T Boundary-clustered interfaces for the Allen–Cahn equation %A Andrea Malchiodi %A Wei-Ming Ni %A Juncheng Wei %B Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 %I Mathematical Sciences Publishers %G en %U http://hdl.handle.net/1963/5089 %1 4905 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-11-17T13:19:29Z\\nNo. of bitstreams: 1\\nmnw-pjm-final.pdf: 287316 bytes, checksum: 2a18e3af66be7b9b793a528138cf493a (MD5) %0 Journal Article %J Adv. Math. 209 (2007) 460-525 %D 2007 %T Concentration on minimal submanifolds for a singularly perturbed Neumann problem %A Fethi Mahmoudi %A Andrea Malchiodi %X We consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $1

1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ → 0. %B Geometric and Functional Analysis 15 (6) 1162-1222 (2005) %I Springer %G en %U http://hdl.handle.net/1963/4866 %1 4645 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-20T13:51:52Z\\nNo. of bitstreams: 1\\nMalchiodi03.pdf: 521628 bytes, checksum: 3aa8a237bad84b04bdd17669f210e057 (MD5) %R 10.1007/s00039-005-0542-7 %0 Journal Article %J C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. %D 2005 %T A fourth order uniformization theorem on some four manifolds with large total Q-curvature %A Zindine Djadli %A Andrea Malchiodi %X Given a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open. %B C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. %I Elsevier %G en %U http://hdl.handle.net/1963/4868 %1 4649 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-20T14:43:43Z\\nNo. of bitstreams: 1\\nexistencep81.pdf: 151457 bytes, checksum: 024bd42cba2f35fe4c206a1ef0f9a125 (MD5) %R 10.1016/j.crma.2005.01.013 %0 Journal Article %J J. Eur. Math. Soc. 7 (2005) 117-144 %D 2005 %T Ground states of nonlinear Schroedinger equations with potentials vanishing at infinity %A Antonio Ambrosetti %A Veronica Felli %A Andrea Malchiodi %X We deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$. %B J. Eur. Math. Soc. 7 (2005) 117-144 %G en_US %U http://hdl.handle.net/1963/2352 %1 1664 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-07T08:16:53Z\\nNo. of bitstreams: 1\\nGround states.pdf: 901500 bytes, checksum: 741c3d55677b872a40e8e3ff2df2a5d2 (MD5) %0 Journal Article %J Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177. %D 2005 %T Minimal surfaces in pseudohermitian geometry %A Jih-Hsin Cheng %A JennFang Hwang %A Andrea Malchiodi %A Paul Yang %X We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set, we formulate some {\em extension} theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the $xy$-plane) in the Heisenberg group $H_1$. In $H_{1}$, identified with the Euclidean space $R^{3}$, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, $C^{2}$ smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard $S^{3}.$ This fact continues to hold when $S^{3}$ is replaced by a general spherical pseudohermitian 3-manifold. %B Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177. %I Scuola Normale Superiore %G en %U http://hdl.handle.net/1963/4579 %1 4347 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-07T09:39:45Z No. of bitstreams: 1 math_0401136v3.pdf: 476553 bytes, checksum: 85c9b54a1f7e6c159e8fbc2486849a53 (MD5) %R 10.2422/2036-2145.2005.1.05 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 %D 2005 %T Multiple clustered layer solutions for semilinear Neumann problems on a ball %A Andrea Malchiodi %A Wei-Ming Ni %A Juncheng Wei %B Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3532 %1 732 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-20T10:15:49Z\\nNo. of bitstreams: 1\\nMalchiodiNiWei04.pdf: 340366 bytes, checksum: a0bb6df9ca59c557fdacb5e7142ecf3d (MD5) %R 10.1016/j.anihpc.2004.05.003 %0 Journal Article %J Duke Math. J. 124 (2004) 105-143 %D 2004 %T Multidimensional boundary layers for a singularly perturbed Neumann problem %A Andrea Malchiodi %A Marcelo Montenegro %B Duke Math. J. 124 (2004) 105-143 %I Duke University Press %G en_US %U http://hdl.handle.net/1963/2960 %1 1740 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-22T08:57:55Z\\nNo. of bitstreams: 1\\nMalchiodiMontenegro03.pdf: 414971 bytes, checksum: a647d87b29bbf0808629d5647dfd1dad (MD5) %R 10.1215/S0012-7094-04-12414-5 %0 Journal Article %J Indiana Univ. Math. J. 53 (2004) 297-392 %D 2004 %T Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %B Indiana Univ. Math. J. 53 (2004) 297-392 %I Indiana University Mathematics Journal %G en %U http://hdl.handle.net/1963/1663 %1 2455 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:06:06Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1512/iumj.2004.53.2400 %0 Journal Article %J C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780 %D 2004 %T Solutions concentrating at curves for some singularly perturbed elliptic problems %A Andrea Malchiodi %B C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780 %I Elsevier %G en %U http://hdl.handle.net/1963/4869 %1 4647 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-20T14:23:50Z\\nNo. of bitstreams: 0 %R 10.1016/j.crma.2004.03.023 %0 Journal Article %J J. Geom. Anal. 13 (2003) 255-289 %D 2003 %T Prescribing scalar and boundary mean curvature on the three dimensional half sphere %A Zindine Djadli %A Andrea Malchiodi %A Mohameden Ould Ahmedou %X We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results. %B J. Geom. Anal. 13 (2003) 255-289 %I Springer %G en_US %U http://hdl.handle.net/1963/3086 %1 1247 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-13T14:32:25Z\\nNo. of bitstreams: 1\\n0211227v1.pdf: 359886 bytes, checksum: e4e0c1b0979d1cb348e41f2351b74254 (MD5) %R 10.1007/BF02930697 %0 Journal Article %J Comm. Math. Phys. 235 (2003) no.3, 427-466 %D 2003 %T Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %B Comm. Math. Phys. 235 (2003) no.3, 427-466 %I Springer %G en %U http://hdl.handle.net/1963/1633 %1 2485 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:37Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1007/s00220-003-0811-y %0 Journal Article %J Interfaces Free Bound. 7 (2002) 345-370 %D 2002 %T Curvature theory of boundary phases: the two-dimensional case %A Andrea Braides %A Andrea Malchiodi %X We describe the behaviour of minimum problems involving non-convex surface integrals in 2D, singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted. %B Interfaces Free Bound. 7 (2002) 345-370 %I European Mathematical Society %G en_US %U http://hdl.handle.net/1963/3537 %1 1164 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T15:34:33Z\\nNo. of bitstreams: 1\\n2001BM.pdf: 361945 bytes, checksum: eb748fdc7f69d6fef497ebaf68f155a6 (MD5) %0 Journal Article %J Commun. Contemp. Math., 2002, 4, 375 %D 2002 %T Prescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result %A Zindine Djadli %A Mohameden Ould Ahmedou %A Andrea Malchiodi %B Commun. Contemp. Math., 2002, 4, 375 %I SISSA Library %G en %U http://hdl.handle.net/1963/1539 %1 2624 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:50Z (GMT). No. of bitstreams: 1\\nmath.AP0101101.pdf: 273679 bytes, checksum: 772598ac956e1f555f866f6330ec1fd6 (MD5)\\n Previous issue date: 2000 %R 10.1142/S0219199702000695 %0 Journal Article %J Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387 %D 2002 %T Prescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications %A Zindine Djadli %A Andrea Malchiodi %A Mohameden Ould Ahmedou %B Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387 %I SISSA Library %G en %U http://hdl.handle.net/1963/1540 %1 2623 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:51Z (GMT). No. of bitstreams: 1\\nmath.AP0104091.pdf: 438502 bytes, checksum: 97c6b7ab20d77a3a40904db3f08928d1 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Calc. Var. Partial Differential Equations 14 (2002), no. 4, 429-445 %D 2002 %T The scalar curvature problem on $S\\\\sp n$: an approach via Morse theory %A Andrea Malchiodi %B Calc. Var. Partial Differential Equations 14 (2002), no. 4, 429-445 %I Springer %G en %U http://hdl.handle.net/1963/1331 %1 3124 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:24Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1007/s005260100110 %0 Journal Article %J Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 %D 2002 %T Singular elliptic problems with critical growth %A Paolo Caldiroli %A Andrea Malchiodi %B Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 %I Dekker %G en %U http://hdl.handle.net/1963/1268 %1 3187 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:34Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1081/PDE-120004887 %0 Journal Article %J C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 %D 2002 %T Solutions concentrating on spheres to symmetric singularly perturbed problems %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %X We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere. %B C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 %I SISSA Library %G en %U http://hdl.handle.net/1963/1594 %1 2524 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:03Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 2002 %R 10.1016/S1631-073X(02)02414-7 %0 Journal Article %J Math. Ann., 2002, 322, 667 %D 2002 %T On the Yamabe problem and the scalar curvature problems under boundary conditions %A Antonio Ambrosetti %A Li YanYan %A Andrea Malchiodi %B Math. Ann., 2002, 322, 667 %I SISSA Library %G en %U http://hdl.handle.net/1963/1510 %1 2653 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:24Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1007/s002080100267 %0 Journal Article %J Asymptotic Anal., 2001, 25, 149-181 %D 2001 %T Adiabatic limits of closed orbits for some Newtonian systems in R-n %A Andrea Malchiodi %X We deal with a Newtonian system like x\\\'\\\' + V\\\'(x) = 0. We suppose that V: \\\\R^n \\\\to \\\\R possesses an (n-1)-dimensional compact manifold M of critical points, and we prove the existence of arbitrarity slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M. %B Asymptotic Anal., 2001, 25, 149-181 %I SISSA Library %G en %U http://hdl.handle.net/1963/1511 %1 2652 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:25Z (GMT). No. of bitstreams: 1\\nmath.DS0006229.pdf: 332070 bytes, checksum: 05767d978ee641c261858a4e235cfeb3 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Nonlinear Anal. 43 (2001) 159-172 %D 2001 %T Multiple positive solutions of some elliptic equations in \\\\bold R\\\\sp N %A Andrea Malchiodi %B Nonlinear Anal. 43 (2001) 159-172 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3094 %1 1239 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-14T10:05:40Z\\nNo. of bitstreams: 1\\nMalchiodixx.pdf: 223149 bytes, checksum: 40e292ff9c4d2277feb12d4615559618 (MD5) %R 10.1016/S0362-546X(99)00186-8 %0 Journal Article %J Arch. Ration. Mech. An., 2001, 159, 253 %D 2001 %T Multiplicity results for some nonlinear Schrodinger equations with potentials %A Antonio Ambrosetti %A Andrea Malchiodi %A Simone Secchi %B Arch. Ration. Mech. An., 2001, 159, 253 %I SISSA Library %G en %U http://hdl.handle.net/1963/1564 %1 2554 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:12Z (GMT). No. of bitstreams: 1\\nmath.AP0011195.pdf: 190473 bytes, checksum: a234c5a09c7dc021355fabc212c8ccb4 (MD5)\\n Previous issue date: 2000 %R 10.1007/s002050100152 %0 Journal Article %J J. Funct. Anal. 180 (2001) 210-241 %D 2001 %T Non-compactness and multiplicity results for the Yamabe problem on Sn %A Massimiliano Berti %A Andrea Malchiodi %B J. Funct. Anal. 180 (2001) 210-241 %I Elsevier %G en %U http://hdl.handle.net/1963/1345 %1 3110 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:35Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1006/jfan.2000.3699 %0 Journal Article %J J. Differential Equations 170 (2001) 228-245 %D 2001 %T On the symmetric scalar curvature problem on S\\\\sp n %A Antonio Ambrosetti %A Andrea Malchiodi %X We discuss some existence results dealing with the scalar curvature problem on S\\\\sp n in the presence of various symmetries. %B J. Differential Equations 170 (2001) 228-245 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3095 %1 1238 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-14T10:19:50Z\\nNo. of bitstreams: 1\\nAmbrosettiMalchiodixx.pdf: 307157 bytes, checksum: 40112a5a91f2314b5e07f647bb5fa92a (MD5) %R 10.1006/jdeq.2000.3816 %0 Thesis %D 2000 %T Existence and multiplicity results for some problems in Riemannian geometry %A Andrea Malchiodi %K Yamabe problem %I SISSA %G en %U http://hdl.handle.net/1963/5948 %1 5808 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-06-22T10:18:59Z\\nNo. of bitstreams: 1\\nPhD_Malchiodi.pdf: 25528908 bytes, checksum: dd49ac5ec54366bb2daf7288eb10f483 (MD5) %] 1 Introduction\\r\\n2 The Yamabe problem: first multiplicity results\\r\\n3 Infinitely many solutions for the Yamabe problem\\r\\n4 The scalar curvature problem: an approach via Morse theory\\r\\n5 The scalar curvature problem: the symmetric case\\r\\n6 Prescribing scalar curvature and boundary mean curvature %0 Journal Article %J Ricerche Mat. 49 (2000), suppl., 169-176 %D 2000 %T A note on the scalar curvature problem in the presence of symmetries %A Antonio Ambrosetti %A Li YanYan %A Andrea Malchiodi %B Ricerche Mat. 49 (2000), suppl., 169-176 %I SISSA Library %G en %U http://hdl.handle.net/1963/1365 %1 3090 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:52Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Cr. Acad. Sci. I-Math, 2000, 330, 1013 %D 2000 %T Scalar curvature under boundary conditions %A Antonio Ambrosetti %A Li YanYan %A Andrea Malchiodi %B Cr. Acad. Sci. I-Math, 2000, 330, 1013 %I SISSA Library %G en %U http://hdl.handle.net/1963/1506 %1 2657 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:21Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1016/S0764-4442(00)00312-8 %0 Journal Article %J J. Funct. Anal. 168 (1999), no. 2, 529-561 %D 1999 %T A multiplicity result for the Yamabe problem on $S\\\\sp n$ %A Antonio Ambrosetti %A Andrea Malchiodi %X We prove a multiplicity result for the Yamabe problem on the manifold (S, g), where g is a perturbation of the standard metric g0 of Sn. Solutions are found by variational methods via an abstract perturbation result. %B J. Funct. Anal. 168 (1999), no. 2, 529-561 %I Elsevier %G en %U http://hdl.handle.net/1963/1264 %1 3191 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:30Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1006/jfan.1999.3458 %0 Journal Article %D 1999 %T On the scalar curvature problem under symmetry %A Antonio Ambrosetti %A Andrea Malchiodi %I SISSA Library %G en %U http://hdl.handle.net/1963/1287 %1 3168 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:48Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999