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...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2022
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Dirichlet probléma, Differenciálegyenlet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2022.1.40 |
| Online Access: | http://acta.bibl.u-szeged.hu/76541 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 20 |
| ISSN: | 1417-3875 |