Boundary singularities of semilinear elliptic equations with Leray-Hardy potential

Huyuan Chen (1) , Laurent Veron (2)

1 Jiangxi Normal University
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

We study existence and uniqueness of solutions of (E 1) −∆u + µ |x| ^{-2} u + g(u) = ν in Ω, u = λ on ∂Ω, where Ω ⊂ R N + is a bounded smooth domain such that 0 ∈ ∂Ω, µ ≥ − N 2 4 is a constant, g a continuous nondecreasing function satisfying some integral growth condition and ν and λ two Radon measures respectively in Ω and on ∂Ω. We show that the situation differs considerably according the measure is concentrated at 0 or not. When g is a power we introduce a capacity framework which provides necessary and sufficient conditions for the solvability of problem (E 1).

Mots clés: Hardy Potential; Radon Measure; Radon Measure. MSC2010: 35B44; 35J75

Domaines: Equations aux dérivées partielles [math.AP]

Huyuan Chen, Laurent Veron. Boundary singularities of semilinear elliptic equations with Leray-Hardy potential. Communications in Contemporary Mathematics, 2022, 24 (7), ⟨10.1142/S0219199721500516⟩. ⟨hal-02301908v2⟩