A priori estimates for complex Hessian equations

Dinew, Sławomir; Kołodziej, Sławomir

doi:10.2140/apde.2014.7.227

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1948-206X (e-only)

ISSN: 2157-5045 (print)

Author Index

To Appear

Other MSP Journals

A priori estimates for complex Hessian equations

Sławomir Dinew and Sławomir Kołodziej

Vol. 7 (2014), No. 1, 227–244

DOI: 10.2140/apde.2014.7.227

Abstract

We prove some $L^{\infty}$ a priori estimates as well as existence and stability theorems for the weak solutions of the complex Hessian equations in domains of $ℂ^{n}$ and on compact Kähler manifolds. We also show optimal $L^{p}$ integrability for $m$ -subharmonic functions with compact singularities, thus partially confirming a conjecture of Błocki. Finally we obtain a local regularity result for $W^{2, p}$ 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.

Keywords

Hessian equation, a priori estimate, pluripotential theory

Mathematical Subject Classification 2010

Primary: 32U15

Secondary: 32U05

Milestones

Received: 6 February 2013

Accepted: 27 November 2013

Published: 7 May 2014

Authors

Sławomir Dinew
Mathematics Department Rutgers Unversity Newark, NJ 07102 United States	Department of Mathematics and Computer Science Jagiellonian University ul. Lojasiewicza 6 30-348 Krakow Poland

Sławomir Kołodziej
Department of Mathematics and Computer Science Jagiellonian University ul Lojasiewicza 6 30-348 Krakow Poland

Vol. 7, No. 1, 2014