Analysis & PDE
- Anal. PDE
- Volume 7, Number 1 (2014), 227-244.
A priori estimates for complex Hessian equations
We prove some a priori estimates as well as existence and stability theorems for the weak solutions of the complex Hessian equations in domains of and on compact Kähler manifolds. We also show optimal integrability for -subharmonic functions with compact singularities, thus partially confirming a conjecture of Błocki. Finally we obtain a local regularity result for solutions of the real and complex Hessian equations under suitable regularity assumptions on the right-hand side. In the real case the method of this proof improves a result of Urbas.
Anal. PDE, Volume 7, Number 1 (2014), 227-244.
Received: 6 February 2013
Accepted: 27 November 2013
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 32U15: General pluripotential theory
Secondary: 32U05: Plurisubharmonic functions and generalizations [See also 31C10]
Dinew, Sławomir; Kołodziej, Sławomir. A priori estimates for complex Hessian equations. Anal. PDE 7 (2014), no. 1, 227--244. doi:10.2140/apde.2014.7.227. https://projecteuclid.org/euclid.apde/1513731472