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Regularity of solutions for a mixed Dirichlet-Signorini problem in a plane polygonal domain. (Régularité des solutions d’un problème mêlé Dirichlet-Signorini dans un domaine polygonal plan.) (French) Zbl 0806.35049
Summary: We prove a regularity result in Hölder spaces for solutions to an elliptic problem with mixed boundary condition, namely Dirichlet on a part of the boundary and Signorini on the remaining part, in a regular or polygonal domain of $$\mathbb{R}^ 2$$. We give the behaviour of the solution near points where the boundary condition type changes.

MSC:
 35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000) 49N60 Regularity of solutions in optimal control 35D10 Regularity of generalized solutions of PDE (MSC2000) 35B65 Smoothness and regularity of solutions to PDEs
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References:
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