Boundary singular solutions of a class of equations with mixed absorption-reaction

Marie-Françoise Bidaut-Veron (1) , Marta Garcia-Huidobro (2) , Laurent Veron (1)

1 IDP - Institut Denis Poisson
2 Departamento de Matemáticas [Santiago de Chile]

We study properties of positive functions satisfying (E) −∆u + u p − M |∇u| q = 0 is a domain Ω or in R N + when p > 1 and 1 < q < min{p, 2}. We concentrate our research on the solutions of (E) vanishing on the boundary except at one point. This analysis depends on the existence of separable solutions in R N +. We consruct various types of positive solutions with an isolated singularity on the boundary. We also study conditions for the removability of compact boundary sets and the Dirichlet problem associated to (E) with a measure for boundary data.

Mots clés: subsolutions; supersolutions; measures; boundary singularities; Subsolutions; Supersolutions; Elliptic equations; Boundary singularities; Bessel capacities; Measures

Domaines: Equations aux dérivées partielles [math.AP]

Marie-Françoise Bidaut-Veron, Marta Garcia-Huidobro, Laurent Veron. Boundary singular solutions of a class of equations with mixed absorption-reaction. Calculus of Variations and Partial Differential, 2022, 61 (113), pp.1-46. ⟨10.1007/s00526-022-02200-z⟩. ⟨hal-02909840v4⟩