Divergence operator and Poincaré inequalities on arbitrary bounded domains
Let Ω be an arbitrary bounded domain of ℝⁿ . We study the right invertibility of the divergence on Ω in weighted Lebesgue and Sobolev spaces on Ω, and rely this invertibility to a geometric characterization of Ω and to weighted Poincare inequalities on Ω. We recover, in particular, well-known result...
Guardado en:
| Autores principales: | , , , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2010
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/127817 |
| Aporte de: |
| Sumario: | Let Ω be an arbitrary bounded domain of ℝⁿ . We study the right invertibility of the divergence on Ω in weighted Lebesgue and Sobolev spaces on Ω, and rely this invertibility to a geometric characterization of Ω and to weighted Poincare inequalities on Ω. We recover, in particular, well-known results on the right invertibility of the divergence in Sobolev spaces when Ω is Lipschitz or, more generally, when Ω is a John domain, and focus on the case of s-John domains. |
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