Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
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 capaci...
| Autores: | ; |
|---|---|
| Tipo de documento: | Artículo |
| Estado: | Published version |
| Fecha de publicación: | 2008 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/138410 |
| Acceso en línea: | https://hdl.handle.net/11441/138410 https://doi.org/10.1016/j.jde.2008.07.027 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Linear degenerate elliptic equations Continuity of solutions Uniform convergence of solutions Maximum principle Homogenization |
| _version_ | 1878737049978142721 |
|---|---|
| author | Briane, Marc |
| author2 | Casado Díaz, Juan |
| author2_role | author |
| author_browse | Briane, Marc Casado Díaz, Juan |
| author_facet | Briane, Marc Casado Díaz, Juan |
| author_role | author |
| collection | idUS. Depósito de Investigación de la Universidad de Sevilla |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_99b66ea35c8a9a7e6e60d2141c39c7d2 |
| institution | Universidad de Sevilla (US) |
| instname_str | Universidad de Sevilla (US) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:idus.us.es:11441/138410 |
| publishDate | 2008 |
| publishDateSort | 2008 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | idUS. Depósito de Investigación de la Universidad de Sevilla |
| spelling | Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients Briane, Marc Casado Díaz, Juan Linear degenerate elliptic equations Continuity of solutions Uniform convergence of solutions Maximum principle Homogenization 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. Elsevier https://hdl.handle.net/11441/138410 https://doi.org/10.1016/j.jde.2008.07.027 |
| spellingShingle | Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients Briane, Marc Linear degenerate elliptic equations Continuity of solutions Uniform convergence of solutions Maximum principle Homogenization |
| status_str | publishedVersion |
| title | Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients |
| title_full | Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients |
| title_fullStr | Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients |
| title_full_unstemmed | Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients |
| title_short | Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients |
| title_sort | Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients |
| topic | Linear degenerate elliptic equations Continuity of solutions Uniform convergence of solutions Maximum principle Homogenization |
| topic_facet | Linear degenerate elliptic equations Continuity of solutions Uniform convergence of solutions Maximum principle Homogenization |
| url | https://hdl.handle.net/11441/138410 https://doi.org/10.1016/j.jde.2008.07.027 |