Maximal solutions for the ∞-eigenvalue problem
In this article we prove that the first eigenvalue of the ∞− Laplacian { min {− ∆ ∞ v, |∇ v |− λ 1 , ∞ (Ω) v } = 0 in Ω v = 0 on ∂ Ω , has a unique (up to scalar multiplication) maximal solution. This maximal solution can be obtained as the limit as ` ↗ 1 of concave problems of the form { min {− ∆ ∞...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/55560 |
| Acesso em linha: | http://hdl.handle.net/11336/55560 |
| Access Level: | acceso abierto |
| Palavra-chave: | maximal solutions infinity laplacian limit problems https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | In this article we prove that the first eigenvalue of the ∞− Laplacian { min {− ∆ ∞ v, |∇ v |− λ 1 , ∞ (Ω) v } = 0 in Ω v = 0 on ∂ Ω , has a unique (up to scalar multiplication) maximal solution. This maximal solution can be obtained as the limit as ` ↗ 1 of concave problems of the form { min {− ∆ ∞ v ` , |∇ v ` |− λ 1 , ∞ (Ω) v ` ` } = 0 in Ω v ` = 0 on ∂ Ω . In this way we obtain that the maximal eigenfunction is the unique one that is the limit of the concave problems as happens for the usual eigenvalue problem for the p − Laplacian for a fixed 1 < p < ∞ . |
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