# Laplace-Beltrami equation on a hypersurface with Lipschitz boundary

## L’équation de Laplace-Beltrami sur une hypersurface avec un bord de Lipschitz

R. Duduchava
The University of Georgia

Published on 28 July 2021   DOI : 10.21494/ISTE.OP.2021.0697

### Mots-clés

Main objective of the present paper is to prove solvability of the Dirichlet, Neumann and Mixed boundary value problems for an anisotropic Laplace-Beltrami equation on a hypersurface ${C}$ with the Lipschitz boundary ${\Gamma=∂C}$ in the classical ${𝕎^1(C)}$ space setting.

Main objective of the present paper is to prove solvability of the Dirichlet, Neumann and Mixed boundary value problems for an anisotropic Laplace-Beltrami equation on a hypersurface ${C}$ with the Lipschitz boundary ${\Gamma=∂C}$ in the classical ${𝕎^1(C)}$ space setting.