We prove an existence and uniqueness theorem for the solution of unilateral problems with L1 data

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L. Boccardo

Dip. di Matematica, Università di Roma 1, Piazza A. Moro 2, 00185 Roma, Italy

G. R. Cirmi

Dip. di Matematica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy

  1. A. Bensoussan, J. L. Lions: Controle Impulsionel et Inequations Quasi Variationnelles, Gauthier-Villars, Paris, 1984.Google Scholar
  2. L. Boccardo, G. R. Cirmi: Nonsmooth unilateral problems, In: Nonsmooth optimization: Methods and Applications (Proceedings Erice 1991), ed. by F. Giannessi, Gordon, Breach (1992) 1-10.https://doi.org/10.4324/9781003580447-1Google Scholar
  3. L. Boccardo, T. Gallouët: Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal. 87 (1989) 149-169.https://doi.org/10.1016/0022-1236(89)90005-0Google Scholar
  4. L. Boccardo, T. Gallouët: Nonlinear elliptic equations with right-hand side measures, Comm. Partial Differential Equations 17 (1992) 641-655.https://doi.org/10.1080/03605309208820857Google Scholar
  5. L. Boccardo, T. Gallouët, L. Orsina: Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996) 539-551.https://doi.org/10.1016/s0294-1449(16)30113-5Google Scholar
  6. C. Brauner, B. Nikolaenko: Homographic approximations of free boundary problems characterized by elliptic variational inequalities, In: Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar III, ed. by H. Brezis, J. L. Lions, Research Notes in Math. 70, Pitman, London (1982) 86-128.Google Scholar
  7. D. Kinderlehrer, G. Stampacchia: An Introduction to Variational Inequalities and their Applications, Academic Press (1980).Google Scholar
  8. H. Lewy, G. Stampacchia: On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math. 22 (1969) 153-188.https://doi.org/10.1002/cpa.3160220203Google Scholar
  9. J. Leray, J. L. Lions: Quelques résultats de Vishik sur les problèmes elliptiques semi-linéaires par les méthodes de Minty et Browder, Bull. Soc. Math. France 93 (1965) 97-107.https://doi.org/10.24033/bsmf.1617Google Scholar

L. Boccardo, G. R. Cirmi. “Existence and Uniqueness of Solution of Unilateral Problems with L^1 Data.” Journal of Convex Analysis 6 (1999), No. 1, 195–206. https://doi.org/10.68381/jca06012