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

Petteri Harjulehto; Peter Hästö

Revista Matemática Complutense (2004)

- Volume: 17, Issue: 1, page 129-146
- ISSN: 1139-1138

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topHarjulehto, 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 -

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