Stability results for obstacle problems with measure data

Leone, Chiara

doi:10.1016/j.anihpc.2005.03.001

Leone, Chiara

Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 6, pp. 679-704.

MR Zbl

DOI : 10.1016/j.anihpc.2005.03.001

@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},
     pages = {679--704},
     publisher = {Elsevier},
     volume = {22},
     number = {6},
     year = {2005},
     doi = {10.1016/j.anihpc.2005.03.001},
     mrnumber = {2172856},
     zbl = {02245283},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2005.03.001/}
}

TY  - JOUR
AU  - Leone, Chiara
TI  - Stability results for obstacle problems with measure data
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2005
SP  - 679
EP  - 704
VL  - 22
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2005.03.001/
DO  - 10.1016/j.anihpc.2005.03.001
LA  - en
ID  - AIHPC_2005__22_6_679_0
ER  -

%0 Journal Article
%A Leone, Chiara
%T Stability results for obstacle problems with measure data
%J Annales de l'I.H.P. Analyse non linéaire
%D 2005
%P 679-704
%V 22
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2005.03.001/
%R 10.1016/j.anihpc.2005.03.001
%G en
%F 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, Tome 22 (2005) no. 6, pp. 679-704. doi : 10.1016/j.anihpc.2005.03.001. https://www.numdam.org/articles/10.1016/j.anihpc.2005.03.001/

Bibliographie
Cité par

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

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

[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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

[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 | Zbl

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

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

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

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

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

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

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

Cité par Sources :