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On solutions of variational inequalities constrained on a subset of positive capacity

Published online by Cambridge University Press:  22 January 2016

Kazuya Hayasida
Affiliation:
Department of Mathematics, Faculty of Science Kanazawa University, Kanazawa 920, Japan
Haruo Nagase
Affiliation:
Department of Mathematics, Faculty of Science Kanazawa University, Kanazawa 920, Japan
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1. Let Ω be a bounded domain of Rn with boundary ∂Ω and let E be a compact subset of Ω. We assume that both ∂Ω and E have positive capacity. The norm and the inner product in L2) are simply denoted by ‖ ‖ and (,) respectively.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[ 1 ] Beirão da Veiga, H., Equazioni ellittiche non lineari con ostacoli sottili, Ann. Scuola Norm. Sup. Pisa, 26 (1972), 533561.Google Scholar
[ 2 ] Brezis, H. and Stampacchia, G., Sur la régularité de la solution d’inéquations elliptiques, Bull. Soc. Math. France, 96 (1968), 153180.Google Scholar
[ 3 ] Caffarelli, G. V., Regolarità di un problema di disequazioni variazionali relativo a due membrance, Lincei Rend., Sci. Fis. Mat. Natur., 50 (1971), 659662.Google Scholar
[ 4 ] Frehse, J., On the regularity of the solution of a second order variational inequality, Boll. Un. Mat. Ital., 6 (1972), 312315.Google Scholar
[ 5 ] Frehse, J., On Signorini’s problem and variational problems with thin obstacles, Ann. Scuola Norm. Sup. Pisa, 4 (1977), 343362.Google Scholar
[ 6 ] Gerhardt, C., Regularity of solutions of nonlinear variational inequalities, Arch. Rational Mech. Anal., 52 (1973), 389393.Google Scholar
[ 7 ] Grisvard, P., Régularité de la solution d’un problème aux limites unilatéral dans un domaine convexe, Séminaire Goulaouic-Schwartz (1975/76), Équations aux dérivées partielles et analyse fonctionelle, Exp. No. 16, 11 pp.Google Scholar
[ 8 ] Hartman, P. and Stampacchia, , On some nonlinear elliptic differential functional equations, Acta Math., 115 (1966), 271310.Google Scholar
[ 9 ] Kinderlehrer, D. and Stampacchia, G., An introduction to variational inequalities and their applications, Academic Press, New York, 1980.Google Scholar
[10] Lewy, H., On a variational problem with inequalities on the boundary, J. Math. Mech., 17 (1968), 861884.Google Scholar
[11] Lewy, H. and Stampacchia, G., On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math., 22 (1969), 153188.Google Scholar
[12] Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod Gauthier-Villars, 1969.Google Scholar
[13] Lions, J. L., Partial differential inequalities, Russian Math. Surveys, 27 (1972), 91159.Google Scholar
[14] Marcus, M., The Dirichlet problem in domain whose boundary is partly degenerated, Ann. Mat. Pura Appl., 73 (1966), 159194.CrossRefGoogle Scholar
[15] Williams, G. H., Lipschitz continuous solutions for nonlinear obstacle problems, Math. Z., 154 (1977), 5165.Google Scholar