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

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.

Hypersurface with Lipschitz boundary Anisotropic Laplace Beltrami equation Dirichlet BVP Neumann BVP Mixed type BVP Günter’s derivatives Lax-Milgram lemma Bessel potential spaces

Hypersurface with Lipschitz boundary Anisotropic Laplace Beltrami equation Dirichlet BVP Neumann BVP Mixed type BVP Günter’s derivatives Lax-Milgram lemma Bessel potential spaces