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

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 χ-plurisubharmonic solutions.

complex Hessian equation, second order estimate
Mathematical Subject Classification 2010
Primary: 35J15, 35J60, 58J05, 35J96
Received: 4 January 2016
Revised: 29 April 2016
Accepted: 28 May 2016
Published: 7 November 2016
Duong H. Phong
Department of Mathematics
Columbia University
New York, NY 10027
United States
Sebastien Picard
Department of Mathematics
Columbia University
New York, NY 10027
United States
Xiangwen Zhang
Department of Mathematics
University of California
Irvine, CA 92697
United States