Analysis & PDE

  • Anal. PDE
  • Volume 9, Number 7 (2016), 1693-1709.

A second order estimate for general complex Hessian equations

Duong Phong, Sebastien Picard, and Xiangwen Zhang

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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.

Article information

Anal. PDE, Volume 9, Number 7 (2016), 1693-1709.

Received: 4 January 2016
Revised: 29 April 2016
Accepted: 28 May 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J15: Second-order elliptic equations 35J60: Nonlinear elliptic equations 58J05: Elliptic equations on manifolds, general theory [See also 35-XX] 35J96: Elliptic Monge-Ampère equations

complex Hessian equation second order estimate


Phong, Duong; Picard, Sebastien; Zhang, Xiangwen. A second order estimate for general complex Hessian equations. Anal. PDE 9 (2016), no. 7, 1693--1709. doi:10.2140/apde.2016.9.1693.

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