We discuss existence, uniqueness, regularity and boundary behaviour of solutions of the Dirichlet problem for the prescribed anisotropic mean curvature equation \begin{equation*} {\rm -div}\left({\nabla u}/{\sqrt{1 + |\nabla u|^2}}\right) = -au + {b}/{\sqrt{1 + |\nabla u|^2}}, \end{equation*} where $a,b>0$ are given parameters and $\Omega$ is a bounded Lipschitz domain in $\RR^N$. This equation appears in the modeling theory of capillarity phenomena for compressible fluids and in the description of the geometry of the human cornea.
Titolo: | The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions |
Autori: | |
Data di pubblicazione: | 2016 |
Rivista: | |
Abstract: | We discuss existence, uniqueness, regularity and boundary behaviour of solutions of the Dirichlet problem for the prescribed anisotropic mean curvature equation \begin{equation*} {\rm -div}\left({\nabla u}/{\sqrt{1 + |\nabla u|^2}}\right) = -au + {b}/{\sqrt{1 + |\nabla u|^2}}, \end{equation*} where $a,b>0$ are given parameters and $\Omega$ is a bounded Lipschitz domain in $\RR^N$. This equation appears in the modeling theory of capillarity phenomena for compressible fluids and in the description of the geometry of the human cornea. |
Handle: | http://hdl.handle.net/11368/2848504 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jde.2015.11.024 |
URL: | http://www.sciencedirect.com/science/article/pii/S0022039615006300 |
Appare nelle tipologie: | 1.1 Articolo in Rivista |
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