Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data
Oppezzo, Pirro ; Rossi, Anna Maria
Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003), p. 415-433 / Harvested from 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.

Publié le : 2003-06-01
@article{BUMI_2003_8_6B_2_415_0,
     author = {Pirro Oppezzo and Anna Maria Rossi},
     title = {Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {6-A},
     year = {2003},
     pages = {415-433},
     zbl = {1177.35079},
     mrnumber = {1988214},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2003_8_6B_2_415_0}
}
Oppezzo, Pirro; Rossi, Anna Maria. Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data. Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003) pp. 415-433. http://gdmltest.u-ga.fr/item/BUMI_2003_8_6B_2_415_0/

[1] Bènilan, P.-Boccardo, L.-Gallouët, T.-Gariepy, R.-Pierre, M.-L.Vazquez, J., An L1-Theory of Existence and Uniqueness of Solutions of Nonlinear Elliptic Equations, Ann. Sc. Norm. Sup. Pisa (4), 22, no. 2 (1995), 241-273. | MR 1354907 | Zbl 0866.35037

[2] Boccardo, L.-Gallouët, T.-Orsina, L.- 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. | MR 1409661 | Zbl 0857.35126

[3] Boccardo, L.-Gallouët, T.-Orsina, L., Existence and nonexistence of solutions for some nonlinear elliptic equations, J. Anal. Math., 73 (1997), 203-223. | MR 1616410 | Zbl 0898.35035

[4] Dal Maso, G.-Murat, F.-Orsina, L.-Prignet, A., Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 28, no. 4 (1999), 741-808. | MR 1760541 | Zbl 0958.35045

[5] Del Vecchio, T.-Posteraro, M. R., Existence and regularity results for nonlinear elliptic equations with measure data, Adv. Differential Equations, 1, no. 5 (1996), 899-917. | MR 1392010 | Zbl 0856.35044

[6] Leray, J.-Lions, J. L., Quelques resultats de Višik sur les problemes elliptiques semilineaires par les methodes de Minty et Browder, Bull. Soc. Math. France, 93 (1965), 97-107. | MR 194733 | Zbl 0132.10502

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

[8] Oppezzi, P.-Rossi, A. M., Renormalized Solutions for Divergence Problems with L1 Data, Atti Sem. Mat. Fis. Univ. Modena Suppl. Vol., 46 (1998), 889-914. | MR 1645761 | Zbl 0949.35059

[9] Oppezzi, P.-Rossi, A. M., Unilateral problems with measure data: links and convergence, Differential Integral Equations, 14, no. 9 (2001), 1051-1076. | MR 1852871 | Zbl 1034.35057

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

[11] Porretta, A., Existence for elliptic equations in L1 having lower order terms with natural growth, Portugal. Math., 57, no. 2 (2000), 179-190. | MR 1759814 | Zbl 0963.35068