A PRESCRIBED ANISOTROPIC MEAN CURVATURE EQUATION MODELING THE CORNEAL SHAPE: A PARADIGM OF NONLINEAR ANALYSIS

被引：11
作者：
Corsato, Chiara [1 ]
De Coster, Colette [2 ]
Obersnel, Franco [3 ]
Omari, Pierpaolo [3 ]
Soranzo, Alessandro [3 ]
机构：
[1] Univ Trieste, Dipartimento Sci Econ Aziendali Matemat & Stat, Piazzale Europa 1, I-34127 Trieste, Italy
[2] Univ Valenciennes, EA 4015, LAMAV, FR CNRS 2956, F-59313 Valenciennes, France
[3] Univ Trieste, Dipartimento Matemat & Geosci, Sez Matemat & Informat, Via A Valerio 12-1, I-34127 Trieste, Italy
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2018年 / 11卷 / 02期
关键词：
Prescribed anisotropic mean curvature equation; positive solution; Dirichlet boundary condition; generalized solution; classical solution; singular solution; existence; uniqueness; regularity; boundary behaviour; bounded variation function; implicit function theorem; topological degree; variational method; lower and upper solutions; GENERALIZED SOLUTIONS; BOUNDARY-BEHAVIOR; DIRICHLET PROBLEM; REGULARITY; EXISTENCE; SURFACES;
D O I：
10.3934/dcdss.2018013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we survey, complete and refine some recent results concerning the Dirichlet problem for the prescribed anisotropic mean curvature equation -div (del u/root 1+vertical bar del u vertical bar(2)) = -au + b/root 1+vertical bar del u vertical bar(2), in a bounded Lipschitz domain Omega subset of R-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.
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页码：213 / 256
页数：44
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