A uniqueness result for a singular elliptic equation with gradient term
We prove the uniqueness of a solution for a problem whose simplest model is with k ≥ 1, 0 Lz(Ω) and Ω is a bounded domain of N, N ≥ 2. So far, uniqueness results are known for k < 1, while existence holds for any k ≥ 1 and f positive in open sets compactly embedded in a neighbourhood of the bound...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2018 |
| Country: | España |
| Institution: | Universidad Nacional de Educación a Distancia |
| Repository: | e-spacio. Repositorio Institucional de la UNED |
| Language: | English |
| OAI Identifier: | oai:e-spacio.uned.es:20.500.14468/24476 |
| Online Access: | https://hdl.handle.net/20.500.14468/24476 |
| Access Level: | Open access |
| Keyword: | 12 Matemáticas comparison principle nonlinear elliptic equations singular natural growth gradient terms |
| Summary: | We prove the uniqueness of a solution for a problem whose simplest model is with k ≥ 1, 0 Lz(Ω) and Ω is a bounded domain of N, N ≥ 2. So far, uniqueness results are known for k < 1, while existence holds for any k ≥ 1 and f positive in open sets compactly embedded in a neighbourhood of the boundary. We extend the uniqueness results to the k ≥ 1 case and show, with an example, that existence does not hold if f is zero near the boundary. We even deal with the uniqueness result when f is replaced by a nonlinear term λuq with 0 < q < 1 and λ > 0. |
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