×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lions J. L., Quelques méthodes de r’solution de problèmes aux limites non linéaires (1969)
[2] Grisvard P., Elliptic problems in non smooth domains. MOnographs and Studies in Math. (1985) · Zbl 0695.35060
[3] Shamir E., Israel Math. Journal 6 (1968)
[4] Breziz H., MOnotonicity Methods in Hilbert Spaces (1971)
[5] STampacchia G., Equ. ellipt. du second order á coeff.
[6] Moussaoui M., Thse Univ. Nice (1977)
[7] Richardson, D. Thesis Univ.
[8] Caffarelli L. A., Further regularity for the Signorini problem C. P. D. E. 4 (1979) · Zbl 0427.35019
[9] Kindrlhrer D., The smoothness of the solution of the boundary obstacle problem J. M. P. A. 60 (1981)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.