Asymptotic behavior of solutions of fully nonlinear equations over exterior domains

Xiaobiao Jia

doi:10.5802/crmath.138

Équations aux dérivées partielles

Asymptotic behavior of solutions of fully nonlinear equations over exterior domains

Xiaobiao Jia ¹

¹ School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, Henan, China.

Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1187-1197.

Résumé

In this paper, we consider the asymptotic behavior at infinity of solutions of a class of fully nonlinear elliptic equations $F (D^{2} u) = f (x)$ over exterior domains, where the Hessian matrix $(D^{2} u)$ tends to some symmetric positive definite matrix at infinity and $f (x) = O (| x |^{- t})$ at infinity with sharp condition $t > 2$ . Moreover, we also obtain the same result if $(D^{2} u)$ is only very close to some symmetric positive definite matrix at infinity.

Reçu le : 2020-09-04
Révisé le : 2020-10-09
Accepté le : 2020-10-25
Publié le : 2021-01-25

DOI : 10.5802/crmath.138

Classification : 35J60, 35B40

Affiliations des auteurs :

Xiaobiao Jia ¹

¹ School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, Henan, China.

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2020__358_11-12_1187_0,
     author = {Xiaobiao Jia},
     title = {Asymptotic behavior of solutions of fully nonlinear equations over exterior domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1187--1197},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {11-12},
     year = {2020},
     doi = {10.5802/crmath.138},
     language = {en},
}

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Xiaobiao Jia. Asymptotic behavior of solutions of fully nonlinear equations over exterior domains. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1187-1197. doi : 10.5802/crmath.138. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.138/

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