Sobolev inequalities with variable exponent attaining the values 1 and n
We study Sobolev embeddings in the Sobolev space W1,p(·) (Ω) with variable exponent satisfying 1 6 p(x) 6 n. Since the exponent is allowed to reach the values 1 and n, we need to introduce new techniques, combining weak- and strong-type estimates, and a new variable exponent target space scale which...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2008 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:28264 |
| Acceso en línea: | https://ddd.uab.cat/record/28264 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_52208_05 |
| Access Level: | acceso abierto |
| Palabra clave: | Variable exponent Sobolev space Sobolev inequality Limit case |
| Sumario: | We study Sobolev embeddings in the Sobolev space W1,p(·) (Ω) with variable exponent satisfying 1 6 p(x) 6 n. Since the exponent is allowed to reach the values 1 and n, we need to introduce new techniques, combining weak- and strong-type estimates, and a new variable exponent target space scale which features a space of exponential type integrability instead of L∞ at the upper end. |
|---|