| Type de publication : |
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Articles dans des revues avec comité de lecture |
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| Titre : |
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Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients |
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| Auteur(s) : |
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Marc Briane ( ) 1, Juan Casado-Diaz () 2 |
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| Laboratoire : |
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| Résumé : |
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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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Langue du texte
intégral : |
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Anglais |
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| Journal : |
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| Journal of Differential Equations |
| Publisher |
Elsevier |
| ISSN |
0022-0396 (eISSN : 1090-2732) |
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| Audience : |
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internationale |
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| Date de publication : |
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2008 |
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| Volume : |
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245 |
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| Numéro : |
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8 |
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| Page, identifiant, ... : |
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2038-2054 |
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| Mots Clés : |
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Homogenization – Conductivity – Functionals – Dirichlet |
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| Classification : |
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35J70, 35B27 |
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