Problème aux limites de Ventcel dans un domaine non régulier. (Ventcel’s boundary value problem in a non-smooth domain). (French) Zbl 0601.35024

We study Ventcel’s boundary problem for the Laplacian in a non-smooth domain. This is a model for the heat transfer between a solid \(\Omega\) and its environment when the boundary \(\Gamma\) is covered with a thin layer of a material with higher conductibility. When \(\Omega\) is a polygon we give an explicit description of the singularities near a corner. When \(\Omega\) is a bounded convex domain in \({\mathbb{R}}^ n\) we prove the existence and uniqueness of a solution in \(H^ 2(\Omega)\).


35J25 Boundary value problems for second-order elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)