Dirichlet problems with skew-symmetric drift terms
We prove existence of finite energy solutions for a linear Dirichlet problem with a drift and a convection term of the form $A\,E(x)\nabla u + \mathrm{div}(u\,E(x))$, with $A > 0$ and $E$ in $(L^{r}(\Omega ))^{N}$. The result is obtained using a nonlinear function of $u$ as test function, in orde...
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| Language: | English |
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.564/ |
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| author | Boccardo, Lucio Casado-Diaz, Juan Orsina, Luigi |
| author_facet | Boccardo, Lucio Casado-Diaz, Juan Orsina, Luigi |
| author_sort | Boccardo, Lucio |
| collection | DOAJ |
| description | We prove existence of finite energy solutions for a linear Dirichlet problem with a drift and a convection term of the form $A\,E(x)\nabla u + \mathrm{div}(u\,E(x))$, with $A > 0$ and $E$ in $(L^{r}(\Omega ))^{N}$. The result is obtained using a nonlinear function of $u$ as test function, in order to “cancel” this term. |
| format | Article |
| id | doaj-art-aa3dda07f452421f935d7f43d20d5b24 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-aa3dda07f452421f935d7f43d20d5b242025-02-07T11:19:53ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G330130610.5802/crmath.56410.5802/crmath.564Dirichlet problems with skew-symmetric drift termsBoccardo, Lucio0Casado-Diaz, Juan1Orsina, Luigi2Istituto Lombardo & Sapienza Università di Roma, ItalyDepartamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, SpainDipartimento di Matematica, Sapienza Università di Roma, ItalyWe prove existence of finite energy solutions for a linear Dirichlet problem with a drift and a convection term of the form $A\,E(x)\nabla u + \mathrm{div}(u\,E(x))$, with $A > 0$ and $E$ in $(L^{r}(\Omega ))^{N}$. The result is obtained using a nonlinear function of $u$ as test function, in order to “cancel” this term.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.564/Singular driftDirichlet problemsnonlinear test functions |
| spellingShingle | Boccardo, Lucio Casado-Diaz, Juan Orsina, Luigi Dirichlet problems with skew-symmetric drift terms Comptes Rendus. Mathématique Singular drift Dirichlet problems nonlinear test functions |
| title | Dirichlet problems with skew-symmetric drift terms |
| title_full | Dirichlet problems with skew-symmetric drift terms |
| title_fullStr | Dirichlet problems with skew-symmetric drift terms |
| title_full_unstemmed | Dirichlet problems with skew-symmetric drift terms |
| title_short | Dirichlet problems with skew-symmetric drift terms |
| title_sort | dirichlet problems with skew symmetric drift terms |
| topic | Singular drift Dirichlet problems nonlinear test functions |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.564/ |
| work_keys_str_mv | AT boccardolucio dirichletproblemswithskewsymmetricdriftterms AT casadodiazjuan dirichletproblemswithskewsymmetricdriftterms AT orsinaluigi dirichletproblemswithskewsymmetricdriftterms |