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| HAL : hal-00360023, version 1 |
| DOI : 10.1016/j.jde.2008.07.027 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Differential Equations 245, 8 (2008) 2038-2054 |
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| Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients |
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| Marc Briane 1Juan Casado-Diaz 2 |
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| (2008) |
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| This paper deals with the behavior of two-dimensional linear elliptic equations with unbounded (and possibly infinite) coefficients. We prove the uniform convergence of the solutions by truncating the coefficients and using a pointwise estimate of the solutions combined with a two-dimensional capacitary estimate. We give two applications of this result: the continuity of the solutions of two-dimensional linear elliptic equations by a constructive approach. and the density of the continuous functions in the domain of the Gamma-limit of equicoercive diffusion energies in dimension two. We also build two counter-examples which show that the previous results cannot be extended to dimension three. (C) 2008 Elsevier Inc. All rights reserved. |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2 : | Departamento de Ecuaciones Diferenciales y Analysis Numerico (UNIVERSIDAD DE SEVILLA) |
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Universidad de Sevilla |
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| Homogenization – Conductivity – Functionals – Dirichlet |
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| hal-00360023, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00360023 | |
| oai:hal.archives-ouvertes.fr:hal-00360023 | |
| Contributeur : Marie-Annick Guillemer | |
| Soumis le : Mardi 10 Février 2009, 10:33:02 | |
| Dernière modification le : Jeudi 18 Mars 2010, 17:34:57 | |
