Divergence operator and Poincaré inequalities on arbitrary bounded domains
نویسندگان
چکیده
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 relate this invertibility to a geometric characterization of Ω and to weighted Poincaré 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. AMS numbers 2000: Primary, 35C15. Secondary, 35F05, 35F15, 46E35.
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