An optimal Poincaré inequality in L1 for convex domains

For convex domains Ω ⊂ ℝn with diameter d we prove ||u||L1(ω) ≤ d/2||∇u||L1(ω) for any u with zero mean value on ω. We also show that the constant 1/2 in this inequality is optimal.

Guardado en:
Detalles Bibliográficos
Autores principales: Acosta, G., Durán, R.G.
Formato: JOUR
Materias:
Poincaré inequalities
Weighted estimates
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00029939_v132_n1_p195_Acosta
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00029939_v132_n1_p195_Acosta
record_format dspace
spelling todo:paper_00029939_v132_n1_p195_Acosta2023-10-03T13:55:07Z An optimal Poincaré inequality in L1 for convex domains Acosta, G. Durán, R.G. Poincaré inequalities Weighted estimates For convex domains Ω ⊂ ℝn with diameter d we prove ||u||L1(ω) ≤ d/2||∇u||L1(ω) for any u with zero mean value on ω. We also show that the constant 1/2 in this inequality is optimal. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00029939_v132_n1_p195_Acosta
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Poincaré inequalities
Weighted estimates
spellingShingle Poincaré inequalities
Weighted estimates
Acosta, G.
Durán, R.G.
An optimal Poincaré inequality in L1 for convex domains
topic_facet Poincaré inequalities
Weighted estimates
description For convex domains Ω ⊂ ℝn with diameter d we prove ||u||L1(ω) ≤ d/2||∇u||L1(ω) for any u with zero mean value on ω. We also show that the constant 1/2 in this inequality is optimal.
format JOUR
author Acosta, G.
Durán, R.G.
author_facet Acosta, G.
Durán, R.G.
author_sort Acosta, G.
title An optimal Poincaré inequality in L1 for convex domains
title_short An optimal Poincaré inequality in L1 for convex domains
title_full An optimal Poincaré inequality in L1 for convex domains
title_fullStr An optimal Poincaré inequality in L1 for convex domains
title_full_unstemmed An optimal Poincaré inequality in L1 for convex domains
title_sort optimal poincaré inequality in l1 for convex domains
url http://hdl.handle.net/20.500.12110/paper_00029939_v132_n1_p195_Acosta
work_keys_str_mv AT acostag anoptimalpoincareinequalityinl1forconvexdomains
AT duranrg anoptimalpoincareinequalityinl1forconvexdomains
AT acostag optimalpoincareinequalityinl1forconvexdomains
AT duranrg optimalpoincareinequalityinl1forconvexdomains
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