@article {2011,
title = {Planar loops with prescribed curvature: existence, multiplicity and uniqueness results},
journal = {Proceedings of the American Mathematical Society 139 (2011) 4445-4459},
number = {SISSA;08/2010/M},
year = {2011},
publisher = {American Mathematical Society},
keywords = {Plane curves},
doi = {10.1090/S0002-9939-2011-10915-8},
url = {http://hdl.handle.net/1963/3842},
author = {Roberta Musina}
}
@article {2010,
title = {Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials},
number = {SISSA;31/2010/M},
year = {2010},
abstract = {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.},
url = {http://hdl.handle.net/1963/3869},
author = {Mouhamed Moustapha Fall and Roberta Musina}
}
@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 {2009,
title = {Existence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities},
journal = {Nonlinear Anal. 70 (2009) 3002-3007},
number = {SISSA;53/2008/M},
year = {2009},
abstract = {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.},
doi = {10.1016/j.na.2008.12.024},
url = {http://hdl.handle.net/1963/2739},
author = {Roberta Musina}
}
@article {2009,
title = {Hardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions},
journal = {Commun. Contemp. Math. 11 (2009) 993-1007},
number = {SISSA;06/2008/M},
year = {2009},
doi = {10.1142/S0219199709003636},
url = {http://hdl.handle.net/1963/2569},
author = {Marita Gazzini and Roberta Musina}
}
@article {2009,
title = {A note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas},
journal = {J. Funct. Anal. 256 (2009) 2741-2745},
number = {SISSA;45/2008/M},
year = {2009},
doi = {10.1016/j.jfa.2008.08.009},
url = {http://hdl.handle.net/1963/2698},
author = {Roberta Musina}
}
@article {2009,
title = {On a Sobolev type inequality related to the weighted p-Laplace operator},
journal = {J. Math. Anal. Appl. 352 (2009) 99-111},
number = {SISSA;18/2008/M},
year = {2009},
doi = {10.1016/j.jmaa.2008.06.021},
url = {http://hdl.handle.net/1963/2613},
author = {Marita Gazzini and Roberta Musina}
}
@article {2007,
title = {On the Maz\\\'ya inequalities: existence and multiplicity results for an elliptic problem involving cylindrical weights},
number = {SISSA;92/2007/M},
year = {2007},
url = {http://hdl.handle.net/1963/2522},
author = {Marita Gazzini and Roberta Musina}
}
@article {2007,
title = {On the regularity of weak solutions to H-systems},
journal = {Atti .Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 209-219},
number = {SISSA;36/2005/M},
year = {2007},
abstract = {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....},
url = {http://hdl.handle.net/1963/1753},
author = {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 {2004,
title = {The role of the spectrum of the Laplace operator on \\\\S2 in the H-bubble problem},
journal = {J. Anal. Math. 94 (2004) 265-291},
number = {SISSA;30/2003/M},
year = {2004},
publisher = {Hebrew University Magnes Press},
doi = {10.1007/BF02789050},
url = {http://hdl.handle.net/1963/2894},
author = {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 {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}
}
@article {1989,
title = {An approach to the thin obstacle problem for variational functionals depending on vector},
journal = {Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743.},
number = {SISSA;41/89/M},
year = {1989},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/802},
author = {Gianni Dal Maso and Roberta Musina}
}
@article {1989,
title = {Surfaces of minimal area enclosing a given body in R\\\\sp 3.},
journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), no. 3, 331--354 (1990).},
number = {SISSA;23/88/M},
year = {1989},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/619},
author = {Giovanni Mancini and Roberta Musina}
}
@article {1988,
title = {Holes and obstacles},
journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 5 (1988), no. 4, 323-345},
number = {SISSA;20/87/M},
year = {1988},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/501},
author = {Roberta Musina and Giovanni Mancini}
}
@article {1988,
title = {H-surfaces with obstacles. (Italian)},
journal = {Ann. Univ. Ferrara Sez. VII (N.S.) 34 (1988), 1-14},
number = {SISSA;9/87/M},
year = {1988},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/491},
author = {Roberta Musina}
}
@mastersthesis {1988,
title = {Variational Problems with Obstructions},
year = {1988},
school = {SISSA},
url = {http://hdl.handle.net/1963/5832},
author = {Roberta Musina}
}