Nonlinear elliptic equations with measure valued absorption potentials - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa Année : 2019

Nonlinear elliptic equations with measure valued absorption potentials

Résumé

We study the semilinear elliptic equation −∆u + g(u)σ = µ with Dirichlet boundary conditions in a smooth bounded domain where σ is a nonnegative Radon measure, µ a Radon measure and g is an absorbing nonlinearity. We show that the problem is well posed if we assume that σ belongs to some Morrey class. Under this condition we give a general existence result for any bounded measure provided g satisfies a subcritical integral assumption. We study also the supercritical case when g(r) = |r| q−1 r, with q > 1 and µ satisfies an absolute continuity condition expressed in terms of some capacities involving σ. 2010 Mathematics Subject Classification. 35 J 61; 31 B 15; 28 C 05 .
Fichier principal
Vignette du fichier
N-Art-23 revised.pdf (476.89 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02368308 , version 1 (18-11-2019)

Identifiants

Citer

Nicolas Saintier, Laurent Veron. Nonlinear elliptic equations with measure valued absorption potentials. Annali della Scuola Normale Superiore di Pisa, 2019, XXII (5), pp.351-397. ⟨10.2422/2036-2145.201803_007⟩. ⟨hal-02368308⟩
71 Consultations
64 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More