no. G3
Article de recherche - Équations aux dérivées partielles
Dirichlet problems with skew-symmetric drift terms
[Problèmes de Dirichlet avec des termes de drift asymétriques]
Boccardo, Lucio1 ; Casado-Diaz, Juan2 ; Orsina, Luigi3 
1Istituto Lombardo & Sapienza Università di Roma, Italy
2Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain
3Dipartimento di Matematica, Sapienza Università di Roma, Italy
Comptes Rendus. Mathématique, Tome 362 (2024) no. G3, pp. 301-306

We prove existence of finite energy solutions for a linear Dirichlet problem with a drift and a convection term of the form AE(x)∇u+div(uE(x)), with A>0 and E in (L r (Ω)) N . The result is obtained using a nonlinear function of u as test function, in order to “cancel” this term.

Nous prouvons l’existence de solutions d’énergie finie pour un problème de Dirichlet linéaire avec un terme de la forme AE(x)∇u+div(uE(x)), où A>0 et E est dans (L r (Ω)) N . Le résultat est obtenu en utilisant une fonction non linéaire de u comme fonction test, afin d’“annuler” ce terme.

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Révisé le :
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DOI : 10.5802/crmath.564
Keywords: Singular drift, Dirichlet problems, nonlinear test functions

Boccardo, Lucio  1   ; Casado-Diaz, Juan  2   ; Orsina, Luigi  3

1 Istituto Lombardo & Sapienza Università di Roma, Italy
2 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain
3 Dipartimento di Matematica, Sapienza Università di Roma, Italy
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     author = {Boccardo, Lucio and Casado-Diaz, Juan and Orsina, Luigi},
     title = {Dirichlet problems with skew-symmetric drift terms},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {301--306},
     year = {2024},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     number = {G3},
     doi = {10.5802/crmath.564},
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Boccardo, Lucio; Casado-Diaz, Juan; Orsina, Luigi. Dirichlet problems with skew-symmetric drift terms. Comptes Rendus. Mathématique, Tome 362 (2024) no. G3, pp. 301-306. doi: 10.5802/crmath.564

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