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...

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Autores principales: Durán, Ricardo Guillermo, Muschietti, María Amelia, Russ, Emmanuel, Tchamitchian, Philippe
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2010
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Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/127817
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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.