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...

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Detalles Bibliográficos
Autores: Carmona, José, Leonori, Tommaso
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/24476
Acceso en línea:https://hdl.handle.net/20.500.14468/24476
Access Level:acceso abierto
Palabra clave:12 Matemáticas
comparison principle
nonlinear elliptic equations
singular natural growth gradient terms
Descripción
Sumario: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.