Work

On the Laplace equation on bounded subanalytic manifolds

Year: 2024

Type: article

Abstract: We prove a trace formula for integration by parts on subanalytic bounded submanifolds of $${\mathbb {R}}^n$$ R n , possibly non closed. We also establish density results for $${\textbf{W}}^{1,p}_\nabla (M)$$ W ∇ 1 , p ( M ) , M bounded subanalytic manifold, which is the space of the $$L^p$$ L p tangent vector fields v on M for which $$\nabla v$$ ∇ v is $$L^p$$ L p , where $$\nabla $$ ∇ is the divergence operator. We derive from these results some theorems of existence and uniqueness of solutions of the Laplace equation with Dirichlet and Neumann boundary type conditions. We then study the p-Laplace equation, for $$p\in [1,\infty )$$ p ∈ [ 1 , ∞ ) large.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-024-02854-x

Author: Guillaume Valette

Institution: Jagiellonian University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Narodowym Centrum Nauki