@article {2009,
title = {Bubbles with prescribed mean curvature: the variational approach},
number = {SISSA;35/2009/M},
year = {2009},
note = {H-systems, prescribed mean curvature equation, blowup},
url = {http://hdl.handle.net/1963/3659},
author = {Paolo Caldiroli and Roberta Musina}
}
@article {2006,
title = {The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results},
journal = {Arch. Ration. Mech. Anal. 181 (2006) 1-42},
number = {SISSA;79/2004/M},
year = {2006},
doi = {10.1007/s00205-005-0398-x},
url = {http://hdl.handle.net/1963/2252},
author = {Paolo Caldiroli and Roberta Musina}
}
@article {2006,
title = {On Palais-Smale sequences for H-systems: some examples},
journal = {Adv. Differential Equations 11 (2006) 931-960},
number = {SISSA;32/2005/M},
year = {2006},
abstract = {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.},
url = {http://hdl.handle.net/1963/2157},
author = {Paolo Caldiroli and Roberta Musina}
}
@article {2004,
title = {Existence of H-bubbles in a perturbative setting},
journal = {Rev. Mat. Iberoamericana 20 (2004) 611-626},
number = {SISSA;35/2002/M},
year = {2004},
publisher = {SISSA Library},
abstract = {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.},
url = {http://hdl.handle.net/1963/1606},
author = {Paolo Caldiroli and Roberta Musina}
}
@article {2004,
title = {H-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method},
journal = {Duke Math. J. 122 (2004), no. 3, 457--484},
number = {SISSA;36/2002/M},
year = {2004},
publisher = {SISSA Library},
abstract = {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 {\textquoteleft}{\textquoteleft}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 $\\\\varepsilon\\\\to 0$.},
doi = {10.1215/S0012-7094-04-12232-8},
url = {http://hdl.handle.net/1963/1607},
author = {Paolo Caldiroli and Roberta Musina}
}
@article {2002,
title = {Existence of minimal H-bubbles},
journal = {Commun. Contemp. Math. 4 (2002) 177-209},
number = {SISSA;67/00/M},
year = {2002},
publisher = {SISSA Library},
doi = {10.1142/S021919970200066X},
url = {http://hdl.handle.net/1963/1525},
author = {Paolo Caldiroli and Roberta Musina}
}
@article {2002,
title = {Singular elliptic problems with critical growth},
journal = {Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876},
number = {SISSA;54/99/M},
year = {2002},
publisher = {Dekker},
doi = {10.1081/PDE-120004887},
url = {http://hdl.handle.net/1963/1268},
author = {Paolo Caldiroli and Andrea Malchiodi}
}
@article {2001,
title = {Existence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations},
journal = {Adv. Differential Equations 6 (2001), no. 3, 303-326},
number = {SISSA;105/99/M},
year = {2001},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/1319},
author = {Paolo Caldiroli and Roberta Musina}
}
@inbook {2001,
title = {S^2 type parametric surfaces with prescribed mean curvature and minimal energy},
booktitle = {Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkh{\"a}user, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77},
number = {SISSA;34/2002/M},
year = {2001},
publisher = {Birkhauser},
organization = {Birkhauser},
url = {http://hdl.handle.net/1963/1605},
author = {Paolo Caldiroli and Roberta Musina}
}
@article {2001,
title = {Stationary states for a two-dimensional singular Schrodinger equation},
journal = {Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633.},
number = {SISSA;35/99/M},
year = {2001},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/1249},
author = {Paolo Caldiroli and Roberta Musina}
}
@article {2000,
title = {On a Steffen\\\'s result about parametric surfaces with prescribed mean curvature},
number = {SISSA;102/00/M},
year = {2000},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/1558},
author = {Roberta Musina and Paolo Caldiroli}
}