$C^{2,\alpha}$-estimate for Monge-Ampere equations with H\"older-continuous right hand side

Xiuxiong Chen; Yuanqi Wang

$C^{2,\alpha}$-estimate for Monge-Ampere equations with H\"older-continuous right hand side

Analysis of PDEs 2014-06-24 v1 Differential Geometry

Authors: Xiuxiong Chen , Yuanqi Wang

Abstract

We present a somewhat new proof to the $C^{2,\alpha}$ -aprori estimate for the uniform elliptic Monge-Ampere equations, in both the real and complex settings. Our estimates do not need to differentiate the equation, and only depends on the $C^{\alpha^{\prime}}-$ norm of the right hand side of the equation, $0<\alpha<\alpha^{\prime}$ .

Keywords

Monge-Ampère equation C^{2,alpha} estimate Hölder continuous elliptic equation a priori estimate

Cite

@article{arxiv.1406.5825,
  title  = {$C^{2,\alpha}$-estimate for Monge-Ampere equations with H\"older-continuous right hand side},
  author = {Xiuxiong Chen and Yuanqi Wang},
  journal= {arXiv preprint arXiv:1406.5825},
  year   = {2014}
}

Comments

14 pages, comments are welcome

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