Asymptotic behavior of solutions of fully nonlinear equations over exterior domains

Abstract

In this paper, we consider the asymptotic behavior at infinity of solutions of a class of fully nonlinear elliptic equations F (D2u) = f (x) over exterior domains, where the Hessian matrix (D2u) 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 (D2u) is only very close to some symmetric positive definite matrix at infinity. 2020 Mathematics Subject Classification. 35J60, 35B40. Manuscript received 4th September 2020, revised 9th October 2020, accepted 25th October 2020.