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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p286_Drelichman |
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todo:paper_0022247X_v347_n1_p286_Drelichman2023-10-03T14:29:13Z Improved Poincaré inequalities with weights Drelichman, I. Durán, R.G. John domains Reverse doubling weights Weighted Poincaré inequality Weighted Sobolev inequality 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. Fil:Drelichman, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p286_Drelichman |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
John domains Reverse doubling weights Weighted Poincaré inequality Weighted Sobolev inequality |
| spellingShingle |
John domains Reverse doubling weights Weighted Poincaré inequality Weighted Sobolev inequality Drelichman, I. Durán, R.G. Improved Poincaré inequalities with weights |
| topic_facet |
John domains Reverse doubling weights Weighted Poincaré inequality Weighted Sobolev inequality |
| description |
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. |
| format |
JOUR |
| author |
Drelichman, I. Durán, R.G. |
| author_facet |
Drelichman, I. Durán, R.G. |
| author_sort |
Drelichman, I. |
| title |
Improved Poincaré inequalities with weights |
| title_short |
Improved Poincaré inequalities with weights |
| title_full |
Improved Poincaré inequalities with weights |
| title_fullStr |
Improved Poincaré inequalities with weights |
| title_full_unstemmed |
Improved Poincaré inequalities with weights |
| title_sort |
improved poincaré inequalities with weights |
| url |
http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p286_Drelichman |
| work_keys_str_mv |
AT drelichmani improvedpoincareinequalitieswithweights AT duranrg improvedpoincareinequalitieswithweights |
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1807319224874434560 |