We prove that any convex viscosity solution of det D 2 u = 1 outside a bounded domain of R n + tends to a quadratic polynomial at infinity with rate at least xn |x| n if u is a quadratic polynomial on {x n = 0} and satisfies µ|x| 2 ≤ u ≤ µ −1 |x| 2 as |x| → ∞ for some 0 < µ ≤ 1 2 .
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.
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