We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

%B Annales de l'Institut Henri Poincaré C, Analyse non linéaire %V 36 %P 119 - 164 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144918300428 %R https://doi.org/10.1016/j.anihpc.2018.04.003 %0 Journal Article %J Communications in Mathematical Physics %D 2019 %T Two-Dimensional Yang–Mills Theory on Surfaces with Corners in Batalin–Vilkovisky Formalism %A Riccardo Iraso %A Mnev, P. %XIn this paper we recover the non-perturbative partition function of 2D Yang–Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D Yang–Mills theory on surfaces with boundaries and corners in the Batalin–Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting–-the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces–-building blocks–-and choosing a convenient gauge-fixing on the pieces, and assembling back the partition function on the surface, one recovers the known non-perturbative answers for 2D Yang–Mills theory.

%B Communications in Mathematical Physics %8 Mar %G eng %U https://doi.org/10.1007/s00220-019-03392-w %R 10.1007/s00220-019-03392-w %0 Report %D 2018 %T Long time existence for fully nonlinear NLS with small Cauchy data on the circle %A Feola Roberto %A Felice Iandoli %G eng %0 Report %D 2018 %T Observables in the equivariant A-model %A Bonechi, F. %A Cattaneo, A.S. %A Riccardo Iraso %A Maxim Zabzine %G eng %U https://arxiv.org/abs/1807.08659 %0 Book Section %B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %D 2017 %T Dispersive Estimates for Schrödinger Operators with Point Interactions in ℝ3 %A Felice Iandoli %A Raffaele Scandone %E Alessandro Michelangeli %E Gianfausto Dell'Antonio %XThe study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

%B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %I Springer International Publishing %C Cham %P 187–199 %@ 978-3-319-58904-6 %G eng %U https://doi.org/10.1007/978-3-319-58904-6_11 %R 10.1007/978-3-319-58904-6_11 %0 Journal Article %J Biomechanics and Modeling in Mechanobiology %D 2017 %T Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts %A Francesco Ballarin %A Elena Faggiano %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %A Sonia Ippolito %A Roberto Scrofani %B Biomechanics and Modeling in Mechanobiology %V 16 %P 1373-1399 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd0 %R 10.1007/s10237-017-0893-7 %0 Journal Article %J Journal of High Energy Physics %D 2016 %T Comparing Poisson Sigma Model with A-model %A Bonechi, F. %A Cattaneo, A.S. %A Riccardo Iraso %XWe discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

%B Journal of High Energy Physics %V 2016 %P 133 %8 Oct %G eng %U https://doi.org/10.1007/JHEP10(2016)133 %R 10.1007/JHEP10(2016)133 %0 Report %D 2016 %T A fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts %A Francesco Ballarin %A Elena Faggiano %A Andrea Manzoni %A Gianluigi Rozza %A Alfio Quarteroni %A Sonia Ippolito %A Roberto Scrofani %A Carlo Antona %X A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases. %I Submitted %G en %U http://urania.sissa.it/xmlui/handle/1963/35240 %1 35545 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-10-14T23:07:40Z No. of bitstreams: 1 BMMB_SISSA_report.pdf: 16374062 bytes, checksum: 7ee82fd9d989ed91bf9cc721ae2114a0 (MD5) %0 Journal Article %J Computers and Mathematics with Applications %D 2016 %T Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries %A Laura Iapichino %A Alfio Quarteroni %A Gianluigi Rozza %X The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed. %B Computers and Mathematics with Applications %I Elsevier %V 71 %P 430 %8 01/2016 %G en %N 1 %1 35187 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-11-05T14:59:46Z No. of bitstreams: 1 RDF2_reduced.pdf: 3254431 bytes, checksum: 508b8775e27dfb868f1b39c270cb4a6f (MD5) %& 408 %0 Report %D 2015 %T Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization %A Francesco Ballarin %A Elena Faggiano %A Sonia Ippolito %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %A Roberto Scrofani %X In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach. %G en %U http://urania.sissa.it/xmlui/handle/1963/34623 %1 34824 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-10-07T00:30:27Z No. of bitstreams: 1 REPORT.pdf: 10426315 bytes, checksum: 6e5ddf4eb4cacdc7e803c2db1a540fc9 (MD5) %0 Journal Article %D 2014 %T A density result for GSBD and its application to the approximation of brittle fracture energies %A Flaviana Iurlano %XWe present an approximation result for functions u: Ω → ℝ^n belonging to the space GSBD(Ω) ∩ L2(Ω, ℝn) with e(u) square integrable and Hn-1(Ju) finite. The approximating functions uk are piecewise continuous functions such that uk → u in (Formula Presented). As an application, we provide the extension to the vector-valued case of the Γ-convergence result in GSBV(Ω) proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).

%I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34647 %1 34851 %2 Mathematics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-14T17:02:41Z No. of bitstreams: 1 preprint2014.pdf: 543013 bytes, checksum: 1d1170449f762ffdaf48812b31671bc2 (MD5) %R 10.1007/s00526-013-0676-7 %0 Journal Article %J Comptes Rendus Mathematique %D 2014 %T An improvement on geometrical parameterizations by transfinite maps %A Jäggli, C. %A Laura Iapichino %A Gianluigi Rozza %X We present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries. %B Comptes Rendus Mathematique %V 352 %P 263–268 %G eng %R 10.1016/j.crma.2013.12.017 %0 Conference Paper %B ECMI 2014 proceedings %D 2014 %T Reduced basis method for the Stokes equations in decomposable domains using greedy optimization %A Laura Iapichino %A Alfio Quarteroni %A Gianluigi Rozza %A Volkwein, Stefan %B ECMI 2014 proceedings %P 1–7 %G eng %0 Report %D 2013 %T Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity %A Matteo Focardi %A Flaviana Iurlano %K Functions of bounded deformation %XWe provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.

%I SISSA %G en %U http://hdl.handle.net/1963/6615 %1 6573 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Flaviana Iurlano (iurlano@sissa.it) on 2013-05-13T11:26:04Z No. of bitstreams: 1 coesivo17_preprint_SISSA.pdf: 482275 bytes, checksum: 890efd398f9ff18a36d5b18fc90f8107 (MD5) %0 Thesis %D 2013 %T An Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems %A Flaviana Iurlano %K Functions of bounded deformation %I SISSA %G en %1 7203 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Flaviana Iurlano (iurlano@sissa.it) on 2013-10-23T12:46:25Z No. of bitstreams: 1 Iurlano - PhD Thesis.pdf: 1234569 bytes, checksum: e031f9fd97f6a1662f96f1caf2bc564e (MD5) %0 Journal Article %J PloS one. Volume 8, Issue 7, July 2013 : e68078 %D 2013 %T Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus %A Giovanni Iacono %A Claudio Altafini %A Vincent Torre %X Hippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box. %B PloS one. Volume 8, Issue 7, July 2013 : e68078 %I Public Library of Science %G en %U http://hdl.handle.net/1963/7287 %1 7332 %2 Neuroscience %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-14T11:26:18Z No. of bitstreams: 1 journal.pone.0068078.pdf: 1188661 bytes, checksum: 29e83864b33fd1a072fe4ab4da6fcc17 (MD5) %R 10.1371/journal.pone.0068078 %0 Journal Article %J Communications on Pure and Applied Analysis 12 (2013) 1657-1686 %D 2013 %T Fracture models as Gamma-limits of damage models %A Gianni Dal Maso %A Flaviana Iurlano %XWe analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

%B Communications on Pure and Applied Analysis 12 (2013) 1657-1686 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/4225 %1 3952 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-23T11:09:07Z\\r\\nNo. of bitstreams: 1\\r\\nDalMaso_Iurlano_25_M.pdf: 360594 bytes, checksum: a0e0909b1c483748ede26b7e785a1d79 (MD5) %R 10.3934/cpaa.2013.12.1657 %0 Journal Article %J Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83 %D 2012 %T Decompositions of large-scale biological systems based on dynamical properties %A Nicola Soranzo %A Fahimeh Ramezani %A Giovanni Iacono %A Claudio Altafini %X MOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties.\\r\\nRESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems.\\r\\nAVAILABILITY: Original heuristics for the methods investigated are described in the article. %B Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83 %I Oxford University Press %G en %U http://hdl.handle.net/1963/5226 %1 5049 %2 Physics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-16T15:13:23Z\\nNo. of bitstreams: 1\\nSoIaRaAl10.pdf: 185656 bytes, checksum: df5605453eb314d79ada4355b16ad3cd (MD5) %R 10.1093/bioinformatics/btr620 %0 Journal Article %J Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 %D 2012 %T Exploring the low-energy landscape of large-scale signed social networks %A Giuseppe Facchetti %A Giovanni Iacono %A Claudio Altafini %X Analogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers. %B Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 %I SISSA %G en %U http://hdl.handle.net/1963/6504 %1 6451 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:27:42Z (GMT) No. of bitstreams: 0 %R 10.1103/PhysRevE.86.036116 %0 Journal Article %J Proceedings of the National Academy of Sciences of the United States of America. Volume 108, Issue 52, 27 December 2011, Pages 20953-20958 %D 2011 %T Computing global structural balance in large-scale signed social networks. %A Giuseppe Facchetti %A Giovanni Iacono %A Claudio Altafini %K Combinatorial optimization %X Structural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\" %B Proceedings of the National Academy of Sciences of the United States of America. Volume 108, Issue 52, 27 December 2011, Pages 20953-20958 %I National Academy of Sciences %G en %U http://hdl.handle.net/1963/6426 %1 6362 %2 Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-01-25T12:27:12Z\\r\\nNo. of bitstreams: 1\\r\\npnas.1109521108-1.pdf: 1293098 bytes, checksum: 288a1ce2e9407b58249c5ea58a06f31b (MD5) %R 10.1073/pnas.1109521108 %0 Journal Article %J Advances in Calculus of Variations., to appear. %D 2011 %T Fracture and plastic models as Gamma-limits of damage models under different regimes %A Flaviana Iurlano %XWe consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

%B Advances in Calculus of Variations., to appear. %I Walter de Gruyter %G en %U http://hdl.handle.net/1963/5069 %1 4883 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-11-15T11:55:02Z\\r\\nNo. of bitstreams: 1\\r\\nIurlano_59M_2011.pdf: 387080 bytes, checksum: e5aab40ae643ec056bf0adc92bcaa7c8 (MD5) %R 10.1515/acv-2011-0011 %0 Journal Article %J BMC Systems Biology 2010, 4:83 %D 2010 %T Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks %A Giovanni Iacono %A Claudio Altafini %X Background. \\nFor large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.\\nResults. \\nIn this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.\\nConclusion. \\nIn conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks. %B BMC Systems Biology 2010, 4:83 %I BioMed Central %G en_US %U http://hdl.handle.net/1963/4055 %1 347 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-13T10:31:59Z\\nNo. of bitstreams: 1\\n1752-0509-4-83.pdf: 1153140 bytes, checksum: 11a6235e8d975094d5fefbdb911af66b (MD5) %R 10.1186/1752-0509-4-83 %0 Thesis %B Università degli Studi di Trieste and SISSA %D 2010 %T New approximation results for free discontinuity problems %A Flaviana Iurlano %B Università degli Studi di Trieste and SISSA %G eng %9 Master's thesis %0 Journal Article %J Mathematical Models and Methods in Applied Sciences %D 2009 %T Solutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions %A Ianni, Isabella %A Giusi Vaira %XIn this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

%B Mathematical Models and Methods in Applied Sciences %V 19 %P 707-720 %G eng %U https://doi.org/10.1142/S0218202509003589 %R 10.1142/S0218202509003589 %0 Journal Article %J Advanced nonlinear studies %D 2008 %T On concentration of positive bound states for the Schrödinger-Poisson problem with potentials %A Ianni, Isabella %A Giusi Vaira %XWe study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

%B Advanced nonlinear studies %I Advanced Nonlinear Studies, Inc. %V 8 %P 573–595 %G eng %R 10.1515/ans-2008-0305.