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

  • Petteri Harjulehto
  • Peter Hästö
Palabras clave: Sobolev spaces, variable exponent, Poincaré inequality, Sobolev imbedding, continuity

Resumen

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.

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Publicado
2004-06-04
Cómo citar
Harjulehto, P., & Hästö, P. (2004). A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces. Revista Matemática Complutense, 17(1), 129 - 146. https://doi.org/10.5209/rev_REMA.2004.v17.n1.16790
Sección
Artículos