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 - 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 - 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 - Singular elliptic problems with critical growth JF - Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 Y1 - 2002 A1 - Paolo Caldiroli A1 - Andrea Malchiodi PB - Dekker UR - http://hdl.handle.net/1963/1268 U1 - 3187 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 -