Renormalised solutions of nonlinear parabolic problems with L1data: Existence and uniqueness

Royal Society of Edinburgh - Proceedings A

Volumn 127, Issue 6, 1997, Pages 1137-1152

  Blanchard, D ^a   Murat, F ^b  

^a UNIVERSITÉ DE ROUEN   (France)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944441361     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500026986     Document Type: Article

References (17)

1. 1 theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1995), 241-73.
2. D. Blanchard. Truncations and monotonicity methods for parabolic equations. Nonlinear Anal. 21 (1993), 725-43.
3. L. Boccardo and T. Gallouët. On some nonlinear elliptic and parabolic equations involving measure data. J. Funct. Anal. 87 (1989), 149-69.
4. L. Boccardo and T. Gallouët. Nonlinear elliptic equations with right-hand side measures. Comm. Partial Differential Equations 17 (1992), 641-55.
5. L. Boccardo, D. Giachetti, J. I. Diaz and F. Murat. Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms. J. Differential Equations 106 (1993), 215-37.
6. L. Boccardo, F. Murat and J.-P. Puel. Existence results for some quasilinear parabolic equations. Nonlinear Anal. Th. Math. Appl. 13 (1989), 373-92.
7. R. J. DiPerna and P.-L. Lions. On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. of Math. 130 (1989), 321-66.
8. J. Leray and J.-L. Lions. Quelques résultats de Visik sur les problèmes elliptiques non linéaires par les méthodes de Minty et Browder. Bull. Soc. Math. 93 (1965), 97-107.
9. J.-L. Lions. Quelques méthodes de résolution des problèmes aux limites non linéaires (Paris: Dunod et Gauthier-Villars, 1969).
10. P.-L. Lions and F. Murat. Renormalized solutions of nonlinear elliptic equations (to appear).
11. F. Murat. Solutiones renormalizadas de EDP elipticas non lineares (Technical report R93023, Laboratoire d'Analyse Numérique, Paris VI, France, 1993).
12. 1ou mesure. In Comptes rendus du 26ème Congrès national d'analyse numérique. Les Karellis, France, 1994 (Université de Lyon 1, 1994).
13. A. Prignet. Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures. Rend. Mat. 15 (1995), 321-37.
14. J. Serrin. Pathological solutions of elliptic differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1964), 385-7.
15. 1data, to appear.
16. P. Bénilan and F. Bouhsiss. Une remarque sur l'unicité des solutions pour l'opérateur de Serrin. C. R. Acad. Sci. Paris 324 (1997), to appear.
17. 1 data. Nonlinear Analysis Th. Math. Appl. 28 (1997), 1943-54.