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

Publication date: 3 April 2015

Abstract: We establish

C^{2, a l p h a}

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.

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Monge-Ampère equations (35J96)

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