Improved Poincaré inequalities with weights
In this paper we prove that if Ω ∈ Rn is a bounded John domain, the following weighted Poincaré-type inequality holds:under(inf, a ∈ R) {norm of matrix} f (x) - a {norm of matrix}Lq (Ω, w1) ≤ C {norm of matrix} ∇ f (x) d (x)α {norm of matrix}Lp (Ω, w2) where f is a locally Lipschitz function on Ω, d...
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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p286_Drelichman |
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| Sumario: | In this paper we prove that if Ω ∈ Rn is a bounded John domain, the following weighted Poincaré-type inequality holds:under(inf, a ∈ R) {norm of matrix} f (x) - a {norm of matrix}Lq (Ω, w1) ≤ C {norm of matrix} ∇ f (x) d (x)α {norm of matrix}Lp (Ω, w2) where f is a locally Lipschitz function on Ω, d (x) denotes the distance of x to the boundary of Ω, the weights w1, w2 satisfy certain cube conditions, and α ∈ [0, 1] depends on p, q and n. This result generalizes previously known weighted inequalities, which can also be obtained with our approach. © 2008 Elsevier Inc. All rights reserved. |
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