Stability results for obstacle problems with measure data
Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 6, p. 679-704
@article{AIHPC_2005__22_6_679_0,
author = {Leone, Chiara},
title = {Stability results for obstacle problems with measure data},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {22},
number = {6},
year = {2005},
pages = {679-704},
doi = {10.1016/j.anihpc.2005.03.001},
zbl = {02245283},
mrnumber = {2172856},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2005__22_6_679_0}
}

Leone, Chiara. Stability results for obstacle problems with measure data. Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 6, pp. 679-704. doi : 10.1016/j.anihpc.2005.03.001. http://www.numdam.org/item/AIHPC_2005__22_6_679_0/

[1] Attouch H., Picard C., Problemes variationnels et theorie du potential non lineaire, Ann. Faculté Sci. Toùlouse 1 (1979) 89-136. | Numdam | MR 554374 | Zbl 0418.49012

[2] Benedetto J.J., Real Variable and Integration, Teubner, Stuttgart, 1976. | MR 580297 | Zbl 0336.26001

[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. Pisa 22 (1995) 240-273. | Numdam | Zbl 0866.35037

[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. | MR 1452883 | Zbl 0891.35009

[5] L. Boccardo, G.R. Cirmi, Existence and uniqueness of solutions of unilateral problems with ${L}^{1}$-data, Manuscript.

[6] Boccardo L., Galloüet T., Problèmes unilatéraux avec données dans ${L}^{1}$, C. R. Acad. Sci. Paris Sér. I 311 (1990) 617-619. | MR 1081418 | Zbl 0715.49013

[7] Boccardo L., Galloüet T., Orsina L., Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Inst. H. Poincaré 13 (1996) 539-551. | Numdam | MR 1409661 | Zbl 0857.35126

[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. | MR 1145746 | Zbl 0749.49009

[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. | MR 652507 | Zbl 0484.49009

[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. | Zbl 0959.49014

[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. | MR 1040879 | Zbl 0671.35016

[12] R. Cirmi, Convergence of the solutions of nonlinear obstacle problems with ${L}^{1}$-data, Manuscript, 1999.

[13] Dall'Aglio P., Leone C., Obstacle problems with measure data and linear operators, Potential Anal. 17 (2002) 45-64. | MR 1906408 | Zbl 01785625

[14] Dal Maso G., On the integral representation of certain local functionals, Ricerche Mat. 32 (1983) 85-113. | MR 740203 | Zbl 0543.49001

[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. | MR 791845 | Zbl 0582.49008

[16] Dal Maso G., Defranceschi A., Convergence of unilateral problems for monotone operators, J. Anal. Mat. 53 (1989) 269-289. | MR 1014990 | Zbl 0726.35048

[17] Del Vecchio T., On the homogenization of a class of pseudomonotone operators in divergence form, Boll. Un. Mat. Ital. 7 (1991) 369-388. | MR 1111128 | Zbl 0777.47026

[18] Kinderlehrer D., Stampacchia G., An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980. | MR 567696 | Zbl 0457.35001

[19] Leone C., Existence and uniqueness of solutions for nonlinear obstacle problems with measure data, Nonlinear Anal. 43 (2000) 199-215. | MR 1790102 | Zbl 0967.35056

[20] Leone C., On a class of nonlinear obstacle problems with measure data, Commun. Partial Differential Equations 25 (2000) 2259-2286. | MR 1789927 | Zbl 0969.35069

[21] Leone C., Porretta A., Entropy solutions for nonlinear elliptic equations in ${L}^{1}$, Nonlinear Anal. 32 (1998) 325-334. | MR 1610574 | Zbl 01337963

[22] Lions J.L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1969. | MR 259693 | Zbl 0189.40603

[23] Mosco U., Convergence of convex sets and of solutions of variational inequalities, Adv. in Math. 3 (1969) 510-585. | MR 298508 | Zbl 0192.49101

[24] L. Tartar, Cours Peccot au Collège de France, Paris 1977.