Lemrabet, Keddour Problème aux limites de Ventcel dans un domaine non régulier. (Ventcel’s boundary value problem in a non-smooth domain). (French) Zbl 0601.35024 C. R. Acad. Sci., Paris, Sér. I 300, 531-534 (1985). 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 \(H^ 2(\Omega)\). Cited in 12 Documents 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) Keywords:Ventcel’s boundary problem; Laplacian; non-smooth domain; heat transfer; singularities near a corner; existence; uniqueness PDFBibTeX XMLCite \textit{K. Lemrabet}, C. R. Acad. Sci., Paris, Sér. I 300, 531--534 (1985; Zbl 0601.35024)