On generalized Sobolev algebras and their applications.

Séverine Bernard (1) , Silvère Paul Nuiro (2)

1 AOC - Analyse Optimisation Controle
2 GRIMAAG - Groupe de Recherche en Informatique et Mathématiques Appliquées Antilles-Guyane

In the last two decades, many algebras of generalized functions have been constructed, particularly the so-called generalized Sobolev algebras. Our goal is to study the latter and some of their main properties. In this framework, we pose and solve a nonlinear degenerated Dirichlet problem with irregular data such as Dirac generalized functions.

Mots clés: Non positive solution; Sobolev algebra; Non positive solution.; Generalized solution; Nonlinear degenerate Dirichlet problem

Domaines: Mathématiques générales [math.GM]

Séverine Bernard, Silvère Paul Nuiro. On generalized Sobolev algebras and their applications.. Topological Methods in Nonlinear Analysis, 2005, 25 (2), pp.375-390. ⟨hal-00004903⟩