Laplace-Beltrami equation on a hypersurface with Lipschitz boundary

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