Symmetry of solutions of minimal gradient graph equations on punctured space

Zixiao Liu; Jiguang Bao

Symmetry of solutions of minimal gradient graph equations on punctured space

Analysis of PDEs 2021-04-23 v1

Authors: Zixiao Liu , Jiguang Bao

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.

Keywords

minimal gradient graph equations punctured space symmetry of solutions Monge-Ampere equation exterior Dirichlet problem asymptotic behavior

Cite

@article{arxiv.2104.10904,
  title  = {Symmetry of solutions of minimal gradient graph equations on punctured space},
  author = {Zixiao Liu and Jiguang Bao},
  journal= {arXiv preprint arXiv:2104.10904},
  year   = {2021}
}

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