The div-curl lemma “trente ans après”: an extension and an application to the G-convergence of unbounded monotone operators
In this paper new div-curl results are derived. For any open set Ω of RN, N⩾2, we study the limit of the product vn⋅wn where the sequences vn and wn are respectively bounded in Lp(Ω)N and Lq(Ω)N, while divvn and curlwn are compact in some Sobolev spaces, under the condition 1⩽1p+1q⩽1+1N. Our approac...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/139293 |
| Acceso en línea: | https://hdl.handle.net/11441/139293 https://doi.org/10.1016/j.matpur.2009.01.002 |
| Access Level: | acceso abierto |
| Palabra clave: | Div-curl lemma Homogenization Monotone operators |
| Sumario: | In this paper new div-curl results are derived. For any open set Ω of RN, N⩾2, we study the limit of the product vn⋅wn where the sequences vn and wn are respectively bounded in Lp(Ω)N and Lq(Ω)N, while divvn and curlwn are compact in some Sobolev spaces, under the condition 1⩽1p+1q⩽1+1N. Our approach is based on a suitable decomposition of the functions vn and wn, combined with the concentration compactness of P.-L. Lions and a recent result of H. Brezis and J. Van Schaftingen. As a consequence we obtain a new result of G-convergence for unbounded monotone operators of N-Laplacian type. |
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