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arXiv · 1504.00963

$C^{2,\alpha}$ estimates and existence results for certain nonconcave PDE

Vamsi P. Pingali
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Abstract

We establish $C^{2,\alpha}$ estimates for PDE of the form convex $+$ a sum of weakly concave functions of the Hessian, thus generalising a recent result of Collins which is in turn inspired by a theorem of Caffarelli and Yuan. Independently, we also prove an existence result for a certain generalised Monge-Amp\`ere PDE.

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Vamsi P. Pingali. 2015-04-04. $C^{2,\alpha}$ estimates and existence results for certain nonconcave PDE. https://arxiv.org/abs/1504.00963

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