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Problème de Dirichlet pour le laplacien dans un domaine à point cuspide. (Dirichlet problem for the Laplacian in domains with cusp on the boundary). (French) Zbl 0651.35016
U is a 2-dimensional bounded domain the boundary of which contains a turning point (or cup). We study the solution of the Dirichlet problem for the Laplace equation on the domain U when the right-hand side is smooth up to the boundary of U. We obtain results of regularity and asymptotics.
Reviewer: J.L.Steux

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J67 Boundary values of solutions to elliptic equations and elliptic systems
35D10 Regularity of generalized solutions of PDE (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs