Artículo
Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
Autor/es | Briane, Marc
Casado Díaz, Juan |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2008-10-15 |
Fecha de depósito | 2022-10-27 |
Publicado en |
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Resumen | 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 ... 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 Γ-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. |
Cita | Briane, M. y Casado Díaz, J. (2008). Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients. Journal of Differential Equations, 245 (8), 2038-2054. https://doi.org/10.1016/j.jde.2008.07.027. |
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