Nagoya Mathematical Journal

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

Kazuya Hayasida and Haruo Nagase

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Nagoya Math. J., Volume 97 (1985), 51-69.

First available in Project Euclid: 14 June 2005

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Primary: 49A29


Hayasida, Kazuya; Nagase, Haruo. On solutions of variational inequalities constrained on a subset of positive capacity. Nagoya Math. J. 97 (1985), 51--69.

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  • [1] Beirao da Veiga, H., Equazioni ellittiche non lineari con ostacoli sottili, Ann. Scuola Norm. Sup. Pisa, 26 (1972), 533-561.
  • [2] Brezis, H. and Stampacchia, G., Sur la regularity de la solution d'inequations elliptiques, Bull. Soc. Math. France, 96 (1968), 153-180.
  • [3] Caffarelli, G. V., Regolarita di un problema di disequazioni variazionali relativo a due membrance, Lincei Rend., Sci. Fis. Mat. Natur., 50 (1971), 659-662.
  • [4] Frehse. J., On the regularity of the solution of a second order variational in- equality, BolLvUn. Mat. Ital., 6 (1972), 312-315.
  • [5] Frehse. J., On Sinorini's problem and variational problems with thin obstacles, Ann. Scuola Norm. Sup. Pisa, 4 (1977), 343-362.
  • [6] Gerhardt, C, Regularity of solutions of nonlinear variational inequalities, Arch. Rational Mech. Anal., 52 (1973), 389-393.
  • [7] Grisvard, P., Regularity de la solution d'un probleme aux limites unilateral dans un domaine convexe, Seminaire Goulaouic-Schwartz (1975/76), Equations aux derivees partielles et analyse fonctionelle, Exp. No.16, 11pp.
  • [8] Hartman, P. and Stampacchia, On some nonlinear elliptic differential functional equations, Acta Math., 115 (1966), 271-310.
  • [9] Kinderlehrer, D. and Stampacchia, G., An introduction to variational inequalities and their applications, Academic Press, New York, 1980.
  • [10] Lewy, H., On a variational problem with inequalities on the boundary, J. Math. Mech., 17 (1968), 861-884.
  • [11] Lewy, H. and Stampacchia, G., On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math., 22 (1969), 153-188.
  • [12] Lions, J. L., Quelques methodes de resolution des problemes aux limites non lineaires, Dunod Gauthier-Villars, 1969.
  • [13] Partial differential inequalities, Russian Math. Surveys, 27 (1972), 91-159.
  • [14] Marcus, M., The Dirichlet problem in domain whose boundary is partly degener- ated, Ann. Mat. Pura Appl., 73 (1966), 159-194
  • [15] Williams, G. H., Lipschitz continuous solutions for nonlinear obstacle problems, Math. Z., 154 (1977), 51-65. Kazuya Hayasida Department of Mathematics Faculty of Science Kanazawa University Kanazawa 920 Japan Haruo Nagase Suzuka College of Technology Suzuka 510-02 Japan