In this paper we survey, complete and refine some recent results concerning the Dirichlet problem for the prescribed anisotropic mean curvature equation egin{equation*} { m -div}left({ abla u}/{sqrt{1 + | abla u|^2}} ight) = -au + {b}/{sqrt{1 + | abla u|^2}}, end{equation*} in a bounded Lipschitz domain $Omega subset RR^N$, with $a,b>0$ parameters. This equation appears in the description of the geometry of the human cornea, as well as in the modeling theory of capillarity phenomena for compressible fluids. Here we show how various techniques of nonlinear functional analysis can successfully be applied to derive a complete picture of the solvability patterns of the problem.

A prescribed anisotropic mean curvature equation modeling the corneal shape: a paradigm of nonlinear analysis

Corsato, Chiara;DE COSTER, COLETTE;Obersnel, Franco;Omari, Pierpaolo
;
Soranzo, Alessandro
2018-01-01

Abstract

In this paper we survey, complete and refine some recent results concerning the Dirichlet problem for the prescribed anisotropic mean curvature equation egin{equation*} { m -div}left({ abla u}/{sqrt{1 + | abla u|^2}} ight) = -au + {b}/{sqrt{1 + | abla u|^2}}, end{equation*} in a bounded Lipschitz domain $Omega subset RR^N$, with $a,b>0$ parameters. This equation appears in the description of the geometry of the human cornea, as well as in the modeling theory of capillarity phenomena for compressible fluids. Here we show how various techniques of nonlinear functional analysis can successfully be applied to derive a complete picture of the solvability patterns of the problem.
2018
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http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14667
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Descrizione: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series S following peer review. The definitive publisher-authenticated version is available online at:https://www.aimsciences.org/article/doi/10.3934/dcdss.2018013
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2915510
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