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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Special Issue: AUS-ICMS 2020   > Article

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

Abstract

Résumé

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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