A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.

Harjulehto, Petteri, and Hästö, Peter. "A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.." Revista Matemática Complutense 17.1 (2004): 129-146. <http://eudml.org/doc/44531>.

@article{Harjulehto2004,
abstract = {We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e.g. if the exponent p is continuous in the closure of a convex domain. We also give an essentially sharp condition for the exponent p as to when there exists an imbedding from the Sobolev space to the space of bounded functions.},
author = {Harjulehto, Petteri, Hästö, Peter},
journal = {Revista Matemática Complutense},
keywords = {Espacios de funciones lineales; Espacios de Sobolev; Inmersiones; Desigualdad de Poincaré; Sobolev spaces; variable exponent; Poincaré inequality; Sobolev embedding},
language = {eng},
number = {1},
pages = {129-146},
title = {A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.},
url = {http://eudml.org/doc/44531},
volume = {17},
year = {2004},
}

TY - JOUR
AU - Harjulehto, Petteri
AU - Hästö, Peter
TI - A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.
JO - Revista Matemática Complutense
PY - 2004
VL - 17
IS - 1
SP - 129
EP - 146
AB - We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e.g. if the exponent p is continuous in the closure of a convex domain. We also give an essentially sharp condition for the exponent p as to when there exists an imbedding from the Sobolev space to the space of bounded functions.
LA - eng
KW - Espacios de funciones lineales; Espacios de Sobolev; Inmersiones; Desigualdad de Poincaré; Sobolev spaces; variable exponent; Poincaré inequality; Sobolev embedding
UR - http://eudml.org/doc/44531
ER -