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

Xiuxiong Chen; Yuanqi Wang

arxiv: 1406.5825 · v1 · pith:JOJ6CBQSnew · submitted 2014-06-23 · 🧮 math.AP · math.DG

C^(2,α)-estimate for Monge-Ampere equations with H\"older-continuous right hand side

Xiuxiong Chen , Yuanqi Wang This is my paper

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keywords alphaequationequationsestimatehandmonge-ampereprimeright

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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, $0<\alpha<\alpha^{\prime}$.

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C^(2,α)-estimate for Monge-Ampere equations with H\"older-continuous right hand side

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