Trace and boundary singularities of positive solutions of a class of quasilinear equations

Marie-Françoise Bidaut-Véron (1) , Laurent Véron (1)

1 IDP - Institut Denis Poisson

We study properties of positive functions satisfying (E) −∆u+m|∇u| q − u p = 0 is a domain Ω or in R N + when p > 1 and 1 < q < 2. We give sufficient conditions for the existence of a solution to (E) with a nonnegative measure µ as boundary data, and these conditions are expressed in terms of Bessel capacities on the boundary. We also study removable boundary singularities and solutions with an isolated singularity on ∂Ω. The different results depends on two critical exponents for p = p c := N +1 N −1 and for q = q c := N +1 N and on the position of q with respect to 2p p+1. Contents

Mots clés: 2010 Mathematics Subject Classification: 35J62-35J66-35J75-31C15 Elliptic equations; boundary singularities; Bessel capacities; measures; supersolutions; subsolutions

Domaines: Equations aux dérivées partielles [math.AP]

Marie-Françoise Bidaut-Véron, Laurent Véron. Trace and boundary singularities of positive solutions of a class of quasilinear equations. Discrete and Continuous Dynamical Systems - Series A, In press, ⟨10.3934/dcds.2022107⟩. ⟨hal-03540218v2⟩