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/

[1] Ph. Bénilan; L. Boccardo; T. Gallouët; R. Gariepy; M. Pierre; J.L. Vázquez An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Volume 22 (1995), pp. 241-273

[2] L. Boccardo Some nonlinear Dirichlet problems in L1 involving lower order terms in divergence form, Progress in Elliptic and Parabolic Partial Differential Equations (Capri, 1994), Pitman Res. Notes Math. Ser., 350, Longman, Harlow, 1996, pp. 43-57

[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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