Symmetry of solutions of minimal gradient graph equations on punctured space

Zixiao Liu; Jiguang Bao

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arXiv · 2104.10904

Symmetry of solutions of minimal gradient graph equations on punctured space

Zixiao Liu·Jiguang Bao

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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-Amp\`ere equation, inverse harmonic Hessian equation and the special Lagrangian equation. This extends the classification results of Monge-Amp\`ere 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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Zixiao Liu, Jiguang Bao. 2021-04-22. Symmetry of solutions of minimal gradient graph equations on punctured space. https://arxiv.org/abs/2104.10904

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