Oppezzo, Rossi: Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data

Oppezzo, Pirro and Rossi, Anna Maria:
Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data
Bollettino dell'Unione Matematica Italiana Serie 8 6-B (2003), fasc. n.2, p. 415-433, Unione Matematica Italiana (English)
pdf (302 Kb), djvu (217 Kb). | MR1988214 | Zbl 1177.35079

Sunto

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.

Referenze Bibliografiche

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[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 1409661 | Zbl 0857.35126

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[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 1760541 | Zbl 0958.35045

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[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 194733 | Zbl 0132.10502

[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 1645761 | Zbl 0949.35059

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

[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 1759814 | Zbl 0963.35068

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Referenza completa

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Referenze Bibliografiche