Definition and existence of renormalized solutions of elliptic equations with general measure data;Définition et existence de solutions renormalisées d'équations elliptiques dont le second membre est une mesure

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 325, Issue 5, 1997, Pages 481-486

  Dal Maso, Gianni ^a   Murat, François ^b   Orsina, Luigi ^c   Prignet, Alain ^d  

^a SISSA   (Italy)

^b SORBONNE UNIVERSITÉ   (France)

^c SAPIENZA UNIVERSITY OF ROME   (Italy)

^d UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031232279     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(97)88893-3     Document Type: Article

References (11)

1. 1 theory of existence and uniqueness of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 22, pp. 241-273.
2. [2] Boccardo L. and Gallouët T., 1992. Nonlinear elliptic equations with right hand side measures, Comm. Part. Diff. Eq., 17, 1992, pp. 641-655.
3. [3] Boccardo L., Gallouët T. and Orsina L., 1996. Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Inst. Henri Poincaré, Anal. non linéaire, 13, pp. 539-551.
4. 1 data. Application to the H-convergence of parabolic quasi-linear equations, Ann. Mat. Pura ed Appl., 170, pp. 207-240.
5. [5] Dal Maso G., Murat F., Orsina L. and Prignet A. Renormalized solutions of elliptic equations with general measure data, in preparation.
6. [6] Fukushima M., Sato K. and Taniguchi S., 1991. On the closable part of pre-Dirichlet forms and the fine support of the underlying measures, Osaka J. Math., 28, pp. 517-535.
7. [7] Lions J.-L., 1969. Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod et Gauthier-Villars, Paris.
8. [8] Lions P.-L. and Murat F. Solutions renormalisées d'équations elliptiques non linéaires, to appear.
9. [9] Prignet A., 1995. Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. Mat., 15, pp. 321-337.
10. [10] Serrin J., 1964. Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 18, pp. 385-387.
11. [11] Stampacchia G., 1965. Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), 15, pp. 189-258.