quasiconformal mappings and a Bernstein type theorem over exterior domains in $\mathbb{R}^2$

Dongsheng Li; Rulin Liu

quasiconformal mappings and a Bernstein type theorem over exterior domains in $\mathbb{R}^2$

Analysis of PDEs 2023-01-12 v1

Authors: Dongsheng Li , Rulin Liu

Abstract

We establish the H\"{o}lder estimate and the asymptotic behavior at infinity for $K$ -quasiconformal mappings over exterior domains in $\mathbb{R}^2$ . As a consequence, we prove an exterior Bernstein type theorem for fully nonlinear uniformly elliptic equations of second order in $\mathbb{R}^2$ .

Keywords

quasiconformal mappings exterior domains holder estimate asymptotic behavior bernstein type theorem fully nonlinear elliptic equations

Cite

@article{arxiv.2301.04383,
  title  = {quasiconformal mappings and a Bernstein type theorem over exterior domains in $\mathbb{R}^2$},
  author = {Dongsheng Li and Rulin Liu},
  journal= {arXiv preprint arXiv:2301.04383},
  year   = {2023}
}

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