Analysis & PDE

  • Anal. PDE
  • Volume 7, Number 1 (2014), 227-244.

A priori estimates for complex Hessian equations

Sławomir Dinew and Sławomir Kołodziej

Full-text: Open access

Abstract

We prove some L a priori estimates as well as existence and stability theorems for the weak solutions of the complex Hessian equations in domains of n and on compact Kähler manifolds. We also show optimal Lp integrability for m-subharmonic functions with compact singularities, thus partially confirming a conjecture of Błocki. Finally we obtain a local regularity result for W2,p 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.

Article information

Source
Anal. PDE, Volume 7, Number 1 (2014), 227-244.

Dates
Received: 6 February 2013
Accepted: 27 November 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731472

Digital Object Identifier
doi:10.2140/apde.2014.7.227

Mathematical Reviews number (MathSciNet)
MR3219505

Zentralblatt MATH identifier
1297.32020

Subjects
Primary: 32U15: General pluripotential theory
Secondary: 32U05: Plurisubharmonic functions and generalizations [See also 31C10]

Keywords
Hessian equation a priori estimate pluripotential theory

Citation

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


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