Strong solutions for singular Dirichlet elliptic problems

We prove an existence result for strong solutions u ∈ W2,q (Ω) of singular semilinear elliptic problems of the form −∆u = g (·, u) in Ω, u = τ on ∂Ω, where 1 < q < ∞, Ω is a bounded domain in Rn with C 2 boundary, 0 ≤ τ ∈ W 2− 1 q ,q and with g : Ω × (0, ∞) → [0, ∞) belonging to a class of non...

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Bibliographic Details
Main Author: Godoy Tomas
Format: Serial
Published: 2022
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Dirichlet probléma, Differenciálegyenlet
Subjects:
doi:10.14232/ejqtde.2022.1.40

Online Access:http://acta.bibl.u-szeged.hu/76541
Description
Summary:We prove an existence result for strong solutions u ∈ W2,q (Ω) of singular semilinear elliptic problems of the form −∆u = g (·, u) in Ω, u = τ on ∂Ω, where 1 < q < ∞, Ω is a bounded domain in Rn with C 2 boundary, 0 ≤ τ ∈ W 2− 1 q ,q and with g : Ω × (0, ∞) → [0, ∞) belonging to a class of nonnegative Carathéodory functions, which may be singular at s = 0 and also at x ∈ S for some suitable subsets S ⊂ Ω. In addition, we give results concerning the uniqueness and regularity of the solutions. A related problem on punctured domains is also considered.
Physical Description:20
ISSN:1417-3875