The Dirichlet problem for a prescribed anisotropic mean curvature equation

Chiara Corsato (1) , Colette De Coster (2) , Pierpaolo Omari (1)

1 Università degli studi di Trieste = University of Trieste
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

We discuss existence, uniqueness, regularity and boundary behaviour of solutions of the Dirichlet problem for the prescribed anisotropic mean curvature equation −div(∇u/1+|∇u|2)=−au+b/1+|∇u|2, where a,b>0 are given parameters and Ω is a bounded Lipschitz domain in RN. This equation appears in the modeling theory of capillarity phenomena for compressible fluids and in the description of the geometry of the human cornea.

Mots clés: Prescribed anisotropic mean curvature equation; Positive solution; Dirichlet boundary condition; Existence; Uniqueness; Regularity; Boundary behaviour; Bounded variation function; Variational methods

Domaines: Mathématiques [math]

Chiara Corsato, Colette De Coster, Pierpaolo Omari. The Dirichlet problem for a prescribed anisotropic mean curvature equation: : existence, uniqueness and regularity of solutions. Journal of Differential Equations, 2016, 260 (5), pp.4572-4618. ⟨10.1016/j.jde.2015.11.024⟩. ⟨hal-03135815⟩