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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 $$H^ 2(\Omega)$$.

##### MSC:
 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)