Two-Dimensional Div-Curl Results: Application to the Lack of Nonlocal Effects in Homogenization
In this paper, we study the asymptotic behaviour of sequences of conduction problems and sequences of the associated diffusion energies. We prove that, contrary to the three-dimensional case, the boundedness of the conductivity sequence in L1 combined with its equi-coerciveness prevents from the app...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/139297 |
| Acceso en línea: | https://hdl.handle.net/11441/139297 https://doi.org/10.1080/03605300600910423 |
| Access Level: | acceso abierto |
| Palabra clave: | Dirichlet forms Div-curl results Elliptic problems Homogenization -convergence Unbounded coefficients |
| Sumario: | In this paper, we study the asymptotic behaviour of sequences of conduction problems and sequences of the associated diffusion energies. We prove that, contrary to the three-dimensional case, the boundedness of the conductivity sequence in L1 combined with its equi-coerciveness prevents from the appearance of nonlocal effects in dimension two. More precisely, in the two-dimensional case we extend the Murat–Tartar H-convergence which holds for uniformly bounded and equi-coercive conductivity sequences, as well as the compactness result which holds for bounded and equiintegrable conductivity sequences in L1. Our homogenization results are based on extensions of the classical div-curl lemma, which are also specific to the dimension two. |
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