Abstract
In this paper, we establish the existence theorem for the exterior Dirichlet problem for special Lagrangian equations with prescribed asymptotic behavior at infinity. This extends the previous results on Monge–Ampère equations and Hessian equations to special Lagrangian equations in dimensions n≤4, which is from calibrated geometry. More generally, we prove that the result is also true for Hessian quotient equations with 0≤l<k≤n in dimensions n≥3.
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