Electron. J. Diff. Equ., Vol. 2016 (2016), No. 168, pp. 1-10.

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

Vamsi P. Pingali

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. We apply this result to prove a unique continuation result for a generalised Monge-Ampere PDE. Independently, we also prove an existence result for a special case.

Submitted July 15, 2015. Published July 4, 2016.
Math Subject Classifications: 35J60, 35J96.
Key Words: Evans-Krylov-Safonov theory; nonconcave equations; generalised Monge-Ampere equations.

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Vamsi P. Pingali
Department of Mathematics
Indian Institute of Science
Bangalore, India, 560012
email: vpingali@math.jhu.edu

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