Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations
In this work we consider the problems { script Lu = f in Ω, u = 0 in ℝN\Ω, and { ut + script Lu = f in QT ≡ Ω x (0,T), u(x,t) = 0 in (ℝN\Ω) x (0,T), u(x, 0) = 0 in Ω, where script L is a nonlocal differential operator and Ω is a bounded domain in ℝN, with Lipschitz boundary. The main goal of this wo...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| 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:20.500.14468/24457 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/24457 |
| Access Level: | acceso abierto |
| Palabra clave: | 12 Matemáticas Nonlocal operators elliptic equations parabolic equations summability of the solutions |
| Sumario: | In this work we consider the problems { script Lu = f in Ω, u = 0 in ℝN\Ω, and { ut + script Lu = f in QT ≡ Ω x (0,T), u(x,t) = 0 in (ℝN\Ω) x (0,T), u(x, 0) = 0 in Ω, where script L is a nonlocal differential operator and Ω is a bounded domain in ℝN, with Lipschitz boundary. The main goal of this work is to study existence, uniqueness and summability of the solution u with respect to the summability of the datum f. In the process we establish an Lp-theory, for p ≥ 1, associated to these problems and we prove some useful inequalities for the applications. |
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