Stability results for obstacle problems with measure data

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1. [1] Attouch H., Picard C., Problemes variationnels et theorie du potential non lineaire, Ann. Faculté Sci. Toùlouse1 (1979) 89-136. Zbl0418.49012MR554374
2. [2] Benedetto J.J., Real Variable and Integration, Teubner, Stuttgart, 1976. Zbl0336.26001MR580297
3. [3] Benilan L., Boccardo L., Galloüet T., Gariepy R., Pierre M., Vazquez J.L., An $L^1$ theory of existence and uniqueness of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa22 (1995) 240-273. Zbl0866.35037
4. [4] Boccardo L., Homogenization and continuous dependence for Dirichlet problems in $L^1$, in: Partial Differential Equation Methods in Control and Shape Analysis, Lecture Notes in Pure and Appl. Math., vol. 188, Dekker, New York, 1997, pp. 41-52. Zbl0891.35009MR1452883
5. [5] L. Boccardo, G.R. Cirmi, Existence and uniqueness of solutions of unilateral problems with $L^1$-data, Manuscript. Zbl0958.47038
6. [6] Boccardo L., Galloüet T., Problèmes unilatéraux avec données dans $L^1$, C. R. Acad. Sci. Paris Sér. I311 (1990) 617-619. Zbl0715.49013MR1081418
7. [7] Boccardo L., Galloüet T., Orsina L., Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Inst. H. Poincaré13 (1996) 539-551. Zbl0857.35126MR1409661
8. [8] Boccardo L., Murat F., Homogenization of nonlinear unilateral problems, in: Composite media and homogenization theory, Progr. Nonlinear Differential Equations Appl., vol. 5, Birkhäuser Boston, Boston, 1991, pp. 81-105. Zbl0749.49009MR1145746
9. [9] Boccardo L., Murat F., Nouveaux résultats de convergence dans des problèmes unilateraux, in: Nonlinear Partial Differential Equations and their Applications (Collège de France seminar), Pitman Res. Notes Math., vol. 60, 1962, pp. 64-85. Zbl0484.49009MR652507
10. [10] Casado Diaz J., Dal Maso G., A weak notion of convergence in capacity with applications to thin obstacle problems, in: Calculus of Variation and Related Topics (Proceedings Haifa, Israel), Pitman Res. Notes Math. Ser., 1999. Zbl0959.49014
11. [11] Chiadò Piat V., Defranceschi A., Asymptotic behaviour of quasi-linear problems with Neumann boundary conditions on perforated domains, Appl. Anal.36 (1990) 65-87. Zbl0671.35016MR1040879
12. [12] R. Cirmi, Convergence of the solutions of nonlinear obstacle problems with $L^1$-data, Manuscript, 1999. 
13. [13] Dall'Aglio P., Leone C., Obstacle problems with measure data and linear operators, Potential Anal.17 (2002) 45-64. Zbl1290.35131MR1906408
14. [14] Dal Maso G., On the integral representation of certain local functionals, Ricerche Mat.32 (1983) 85-113. Zbl0543.49001MR740203
15. [15] Dal Maso G., Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets, J. Funct. Anal.62 (1985) 119-159. Zbl0582.49008MR791845
16. [16] Dal Maso G., Defranceschi A., Convergence of unilateral problems for monotone operators, J. Anal. Mat.53 (1989) 269-289. Zbl0726.35048MR1014990
17. [17] Del Vecchio T., On the homogenization of a class of pseudomonotone operators in divergence form, Boll. Un. Mat. Ital.7 (1991) 369-388. Zbl0777.47026MR1111128
18. [18] Kinderlehrer D., Stampacchia G., An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980. Zbl0457.35001MR567696
19. [19] Leone C., Existence and uniqueness of solutions for nonlinear obstacle problems with measure data, Nonlinear Anal.43 (2000) 199-215. Zbl0967.35056MR1790102
20. [20] Leone C., On a class of nonlinear obstacle problems with measure data, Commun. Partial Differential Equations25 (2000) 2259-2286. Zbl0969.35069MR1789927
21. [21] Leone C., Porretta A., Entropy solutions for nonlinear elliptic equations in $L^1$, Nonlinear Anal.32 (1998) 325-334. Zbl1155.35352MR1610574
22. [22] Lions J.L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
23. [23] Mosco U., Convergence of convex sets and of solutions of variational inequalities, Adv. in Math.3 (1969) 510-585. Zbl0192.49101MR298508
24. [24] L. Tartar, Cours Peccot au Collège de France, Paris 1977.