Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 415-433.

Voir la notice de l'article dans Biblioteca Digitale Italiana di Matematica

We prove the existence of a renormalized solution for a nonlinear non coercive divergence problem with lower order terms and measure data. In a particular case we also give a uniqueness result.
Si prova l'esistenza di una soluzione rinormalizzata per un problema ellittico nonlineare noncoercivo in forma di divergenza, in presenza di termini di ordine inferiore al secondo e dato misura. In ipotesi più restrittive si ottiene anche un teorema di unicità.
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Oppezzo, Pirro; Rossi, Anna Maria. Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 415-433. https://geodesic-test.mathdoc.fr/item/BUMI_2003_8_6B_2_a9/

[1] P. Bènilan-L. Boccardo-T. Gallouët-R. Gariepy-M. Pierre-J. L.Vazquez, An $L^1$-Theory of Existence and Uniqueness of Solutions of Nonlinear Elliptic Equations, Ann. Sc. Norm. Sup. Pisa (4), 22, no. 2 (1995), 241-273. | fulltext mini-dml | MR | Zbl

[2] L. Boccardo-T. Gallouët-L. Orsina- Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Inst. H. Poincare Anal. Non Lineaire, 13, no. 5 (1996), 539-551. | fulltext mini-dml | MR | Zbl

[3] L. Boccardo-T. Gallouët-L. Orsina, Existence and nonexistence of solutions for some nonlinear elliptic equations, J. Anal. Math., 73 (1997), 203-223. | MR | Zbl

[4] G. Dal Maso-F. Murat-L. Orsina-A. Prignet, Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 28, no. 4 (1999), 741-808. | fulltext mini-dml | MR | Zbl

[5] T. Del Vecchio-M. R. Posteraro, Existence and regularity results for nonlinear elliptic equations with measure data, Adv. Differential Equations, 1, no. 5 (1996), 899-917. | MR | Zbl

[6] J. Leray-J. L. Lions, Quelques resultats de Višik sur les problemes elliptiques semilineaires par les methodes de Minty et Browder, Bull. Soc. Math. France, 93 (1965), 97-107. | fulltext mini-dml | MR | Zbl

[7] F. Murat, Soluciones renormalizadas de EDP elipticas no lineales, Publications du Laboratoire d'Analyse Numerique n. 93023, Universite Pierre et Marie Curie, Paris (1993).

[8] P. Oppezzi-A. M. Rossi, Renormalized Solutions for Divergence Problems with $L^1$ Data, Atti Sem. Mat. Fis. Univ. Modena Suppl. Vol., 46 (1998), 889-914. | MR | Zbl

[9] P. Oppezzi-A. M. Rossi, Unilateral problems with measure data: links and convergence, Differential Integral Equations, 14, no. 9 (2001), 1051-1076. | MR | Zbl

[10] P. Oppezzi-A. M. Rossi, Renormalized Solutions for Equations with Lower Order Terms and Measure Data, preprint n. 411, DIMA, Università di Genova, April 2000.

[11] A. Porretta, Existence for elliptic equations in $L^1$ having lower order terms with natural growth, Portugal. Math., 57, no. 2 (2000), 179-190. | MR | Zbl