Comptes Rendus
no. 5
Partial Differential Equations
A uniqueness result for monotone elliptic problems
[Un résultat d'unicité pour des problèmes elliptiques monotones]

Présenté par : Haïm Brezis

Maria Michaela Porzio1
1 Facoltá di Scienze, Università del Sannio, via Port'Arsa 11, 82100 Benevento, Italy
Comptes Rendus. Mathématique, Volume 337 (2003) no. 5, pp. 313-316.

Nous donnons une demonstration très simple de l'unicité des solutions entropiques de problèmes de Dirichlet dans L1.

We give here a short proof of the uniqueness of entropy solutions for nonlinear monotone elliptic problems with L1-data.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00347-9

Maria Michaela Porzio 1

1 Facoltá di Scienze, Università del Sannio, via Port'Arsa 11, 82100 Benevento, Italy 
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Maria Michaela Porzio. A uniqueness result for monotone elliptic problems. Comptes Rendus. Mathématique, Volume 337 (2003) no. 5, pp. 313-316. doi : 10.1016/S1631-073X(03)00347-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00347-9/

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[3] H. Brezis; W.A. Strauss Semi-linear second-order elliptic equations in L1, J. Math. Soc. Japan, Volume 25 (1973) no. 4, pp. 565-590

[4] A. Prignet Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. Mat., Volume 15 (1995), pp. 321-337

[5] J. Serrin Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Volume 18 (1964), pp. 385-387

[6] G. Stampacchia Le probléme de Dirichlet pour les équations elliptiques du second ordre á coefficients discontinus, Ann. Inst. Fourier (Grenoble), Volume 15 (1965), pp. 189-258

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