Improvement of Besov regularity for solutions of the fractional Laplacian
We prove a mean value formula for weak solutions of div(|y| agradu) = 0 in Rn+1 = {(x, y) : x ∈ Rn, y ∈ R}, −1 < a < 1, and balls centered at points of the form (x, 0). We obtain an explicit nonlocal kernel for the mean value formula for solutions of (−)s f = 0 on a domain D of Rn. When D is L...
| Autores: | , , |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2014 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/9379 |
| Acesso em linha: | http://hdl.handle.net/11336/9379 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Degenerate Elliptic Equations Fractional Laplacian Mean Value Formula Besov Spaces Gradient Estimates https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | We prove a mean value formula for weak solutions of div(|y| agradu) = 0 in Rn+1 = {(x, y) : x ∈ Rn, y ∈ R}, −1 < a < 1, and balls centered at points of the form (x, 0). We obtain an explicit nonlocal kernel for the mean value formula for solutions of (−)s f = 0 on a domain D of Rn. When D is Lipschitz, we prove a Besov type regularity improvement for the solutions of (−)s f = 0. |
|---|