A prescribed anisotropic mean curvature equation modeling the corneal shape: A paradigm of nonlinear analysis
Résumé
In this paper we survey, complete and refine some recent results concerning the Dirichlet problem for the prescribed anisotropic mean curvature equation (Equation Presented), in a bounded Lipschitz domain Ω ⊂ RN, 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.
Mots clés
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.