The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ and we prove that for the first eigenvalue λ1,p we have (λ1,p)1/p→λ∞=1/maxx∈Ωd...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/59873 |
| Acceso en línea: | http://hdl.handle.net/11336/59873 |
| Access Level: | acceso abierto |
| Palabra clave: | INFINITY LAPLACIAN NONLINEAR EIGENVALUE PROBLEM P-LAPLACIAN VISCOSITY SOLUTIONS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ and we prove that for the first eigenvalue λ1,p we have (λ1,p)1/p→λ∞=1/maxx∈Ωdist(x,∂Ω).Concerning the eigenfunctions (up, vp) associated with λ1,p normalized by ∫Ω|up|α|vp|β=1, there is a uniform limit (u∞, v∞) that is a solution to a limit minimization problem as well as a viscosity solution to (Formula presented.) In addition, we also analyze the limit PDE when we consider higher eigenvalues. |
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