Comptes Rendus
Existence and uniqueness results for nonlinear elliptic problems with a lower order term and measure datum
[Existence et unicité de solutions renormalisées d'équations elliptiques non linéaires avec des termes d'ordre inférieur et données mesures]
Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 757-762.

Dans cette Note nous considérons une classe de problèmes non linéaires et non coercifs dont le prototype est

- p u+b(x)|u| λ =μ dans Ω,u=0 sur Ω,
Ω est un ouvert borné de N (N⩾2), △p est le p-Laplacien (1<p<N) ou une variante de cet opérateur, μ est une mesure de Radon bornée ou une function de L 1 (Ω), λ⩾0 et b appartient à l'espace de Lorentz L N,1 (Ω) ou à l'espace de Lebesgue L (Ω). Nous démontrons l'existence et l'unicité de solutions renormalisées de ce problème.

In this Note we consider a class of noncoercive nonlinear problems whose prototype is

- p u+b(x)|u| λ =μ in Ω,u=0 on Ω,
where Ω is a bounded open subset of N (N⩾2), △p is the so called p-Laplace operator (1<p<N) or a variant of it, μ is a Radon measure with bounded variation on Ω or a function in L 1 (Ω), λ⩾0 and b belongs to the Lorentz space L N,1 (Ω) or to the Lebesgue space L (Ω). We prove existence and uniqueness of renormalized solutions.

Reçu le :
Révisé le :
Publié le :
DOI : 10.1016/S1631-073X(02)02338-5

M.Francesca Betta 1 ; Anna Mercaldo 2 ; François Murat 3 ; M.Michaela Porzio 4

1 Dipartimento di Matematica, Seconda Università di Napoli, via Vivaldi 43, 81100 Caserta, Italy
2 Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, via Cintia, 80126 Napoli, Italy
3 Laboratoire Jacques-Louis Lions, Université Paris VI, boı̂te courrier 187, 75252 Paris cedex 05, France
4 Facoltà di Scienze Matematiche, Fisiche e Naturali, Università degli Studi del Sannio, via Port'Arsa 11, 82100 Benevento, Italy
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     title = {Existence and uniqueness results for nonlinear elliptic problems with a lower order term and measure datum},
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M.Francesca Betta; Anna Mercaldo; François Murat; M.Michaela Porzio. Existence and uniqueness results for nonlinear elliptic problems with a lower order term and measure datum. Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 757-762. doi : 10.1016/S1631-073X(02)02338-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02338-5/

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