Symmetry of solutions of minimal gradient graph equations on punctured space

Abstract

In this paper, we study symmetry and existence of solutions of minimal gradient graph equations on punctured space ${\mathbb{R}}^n\setminus \{0\}$, which include the Monge-Ampère equation, inverse harmonic Hessian equation and the special Lagrangian equation. This extends the classification results of Monge-Ampère equations. Under some conditions, we also give the characterization of the solvability on exterior Dirichlet problem in terms of their asymptotic behaviors.

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Cited by in corpus (1)

• Asymptotic expansion and optimal symmetry of minimal gradient graph equations in dimension 2