Asymptotic behavior of solutions of fully nonlinear equations over exterior domains

Jia, Xiaobiao

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

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

Classification : 35J60, 35B40

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