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...

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Detalles Bibliográficos
Autores: Briane, Marc, Casado Díaz, Juan, Murat, François
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
Descripción
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.