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 -