#### Vol. 9, No. 7, 2016

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A second order estimate for general complex Hessian equations

### Duong H. Phong, Sebastien Picard and Xiangwen Zhang

Vol. 9 (2016), No. 7, 1693–1709
DOI: 10.2140/apde.2016.9.1693
##### Abstract

We consider the general complex Hessian equations with right-hand sides depending on gradients, which are motivated by the Fu–Yau equations arising from the study of Strominger systems. The second order estimate for the solution is crucial to solving the equation by the method of continuity. We obtain such an estimate for the $\chi$-plurisubharmonic solutions.

##### Keywords
complex Hessian equation, second order estimate
##### Mathematical Subject Classification 2010
Primary: 35J15, 35J60, 58J05, 35J96