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2014 A priori estimates for complex Hessian equations
Sławomir Dinew, Sławomir Kołodziej
Anal. PDE 7(1): 227-244 (2014). DOI: 10.2140/apde.2014.7.227

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.

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Sławomir Dinew. Sławomir Kołodziej. "A priori estimates for complex Hessian equations." Anal. PDE 7 (1) 227 - 244, 2014. https://doi.org/10.2140/apde.2014.7.227

Information

Received: 6 February 2013; Accepted: 27 November 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1297.32020
MathSciNet: MR3219505
Digital Object Identifier: 10.2140/apde.2014.7.227

Subjects:
Primary: 32U15
Secondary: 32U05

Keywords: a priori estimate , Hessian equation , pluripotential theory

Rights: Copyright © 2014 Mathematical Sciences Publishers

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