TY - JOUR T1 - Planar loops with prescribed curvature: existence, multiplicity and uniqueness results JF - Proceedings of the American Mathematical Society 139 (2011) 4445-4459 Y1 - 2011 A1 - Roberta Musina KW - Plane curves PB - American Mathematical Society UR - http://hdl.handle.net/1963/3842 U1 - 867 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials Y1 - 2010 A1 - Mouhamed Moustapha Fall A1 - Roberta Musina AB - In this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results. UR - http://hdl.handle.net/1963/3869 U1 - 840 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Bubbles with prescribed mean curvature: the variational approach Y1 - 2009 A1 - Paolo Caldiroli A1 - Roberta Musina UR - http://hdl.handle.net/1963/3659 N1 - H-systems, prescribed mean curvature equation, blowup U1 - 646 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities JF - Nonlinear Anal. 70 (2009) 3002-3007 Y1 - 2009 A1 - Roberta Musina AB - This paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984. UR - http://hdl.handle.net/1963/2739 U1 - 1961 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Hardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions JF - Commun. Contemp. Math. 11 (2009) 993-1007 Y1 - 2009 A1 - Marita Gazzini A1 - Roberta Musina UR - http://hdl.handle.net/1963/2569 U1 - 1551 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas JF - J. Funct. Anal. 256 (2009) 2741-2745 Y1 - 2009 A1 - Roberta Musina UR - http://hdl.handle.net/1963/2698 U1 - 1402 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On a Sobolev type inequality related to the weighted p-Laplace operator JF - J. Math. Anal. Appl. 352 (2009) 99-111 Y1 - 2009 A1 - Marita Gazzini A1 - Roberta Musina UR - http://hdl.handle.net/1963/2613 U1 - 1510 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - On the Maz\\\'ya inequalities: existence and multiplicity results for an elliptic problem involving cylindrical weights Y1 - 2007 A1 - Marita Gazzini A1 - Roberta Musina UR - http://hdl.handle.net/1963/2522 U1 - 1596 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the regularity of weak solutions to H-systems JF - Atti .Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 209-219 Y1 - 2007 A1 - Roberta Musina AB - Abstract. In this paper we prove that every weak solution to the H-surface equation is locally bounded, provided the prescibed mean curvatore H is asymptotic to a constant at infinity (with a suitable decay rate). No smoothness ssumptions are required on H. We consider also the Dirichlet problem.... UR - http://hdl.handle.net/1963/1753 U1 - 2791 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results JF - Arch. Ration. Mech. Anal. 181 (2006) 1-42 Y1 - 2006 A1 - Paolo Caldiroli A1 - Roberta Musina UR - http://hdl.handle.net/1963/2252 U1 - 1995 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On Palais-Smale sequences for H-systems: some examples JF - Adv. Differential Equations 11 (2006) 931-960 Y1 - 2006 A1 - Paolo Caldiroli A1 - Roberta Musina AB - We exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour. UR - http://hdl.handle.net/1963/2157 U1 - 2087 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of H-bubbles in a perturbative setting JF - Rev. Mat. Iberoamericana 20 (2004) 611-626 Y1 - 2004 A1 - Paolo Caldiroli A1 - Roberta Musina AB - Given a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function. PB - SISSA Library UR - http://hdl.handle.net/1963/1606 U1 - 2512 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - H-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method JF - Duke Math. J. 122 (2004), no. 3, 457--484 Y1 - 2004 A1 - Paolo Caldiroli A1 - Roberta Musina AB - Given a regular function $H\\\\colon\\\\mathbb{R}^{3}\\\\to\\\\mathbb{R}$, we look for $H$-bubbles, that is, regular surfaces in $\\\\mathbb{R}^{3}$ parametrized on the sphere $\\\\mathbb{S}+^{2}$ with mean curvature $H$ at every point. Here we study the case of $H(u)=H_{0}+\\\\varepsilon H_{1}(u)=:H_{\\\\varepsilon}(u)$, where $H_{0}$ is a nonzero constant, $\\\\varepsilon$ is the smallness parameter, and $H_{1}$ is any $C^{2}$-function. We prove that if $\\\\bar p\\\\in\\\\mathbb{R}^{3}$ is a ``good\\\'\\\' stationary point for the Melnikov-type function $\\\\Gamma(p)=-\\\\int_{|q-p|<|H_{0}|^{-1}}H_{1}(q)\\\\,dq$, then for $|\\\\varepsilon|$ small there exists an $H_{\\\\varepsilon}$-bubble $\\\\omega^{\\\\varepsilon}$ that converges to a sphere of radius $|H_{0}|^{-1}$ centered at $\\\\bar p$, as $\\\\varepsilon\\\\to 0$. PB - SISSA Library UR - http://hdl.handle.net/1963/1607 U1 - 2511 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The role of the spectrum of the Laplace operator on \\\\S2 in the H-bubble problem JF - J. Anal. Math. 94 (2004) 265-291 Y1 - 2004 A1 - Roberta Musina PB - Hebrew University Magnes Press UR - http://hdl.handle.net/1963/2894 U1 - 1806 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of minimal H-bubbles JF - Commun. Contemp. Math. 4 (2002) 177-209 Y1 - 2002 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1525 U1 - 2638 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations JF - Adv. Differential Equations 6 (2001), no. 3, 303-326 Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1319 U1 - 3136 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - S^2 type parametric surfaces with prescribed mean curvature and minimal energy T2 - Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina JF - Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 PB - Birkhauser UR - http://hdl.handle.net/1963/1605 U1 - 2513 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stationary states for a two-dimensional singular Schrodinger equation JF - Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633. Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1249 U1 - 3206 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On a Steffen\\\'s result about parametric surfaces with prescribed mean curvature Y1 - 2000 A1 - Roberta Musina A1 - Paolo Caldiroli PB - SISSA Library UR - http://hdl.handle.net/1963/1558 U1 - 2560 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An approach to the thin obstacle problem for variational functionals depending on vector JF - Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. Y1 - 1989 A1 - Gianni Dal Maso A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/802 U1 - 2989 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Surfaces of minimal area enclosing a given body in R\\\\sp 3. JF - Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), no. 3, 331--354 (1990). Y1 - 1989 A1 - Giovanni Mancini A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/619 U1 - 3285 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Holes and obstacles JF - Ann. Inst. H. Poincare Anal. Non Lineaire 5 (1988), no. 4, 323-345 Y1 - 1988 A1 - Roberta Musina A1 - Giovanni Mancini PB - SISSA Library UR - http://hdl.handle.net/1963/501 U1 - 3403 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - H-surfaces with obstacles. (Italian) JF - Ann. Univ. Ferrara Sez. VII (N.S.) 34 (1988), 1-14 Y1 - 1988 A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/491 U1 - 3413 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Variational Problems with Obstructions Y1 - 1988 A1 - Roberta Musina PB - SISSA UR - http://hdl.handle.net/1963/5832 U1 - 5683 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER -