Work

A priori estimates for complex Hessian equations

Year: 2014

Type: article

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 ‫ރ‬ 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.

Source: Analysis & PDE

DOI: 10.2140/apde.2014.7.227

Authors: Sławomir Dinew, Sławomir Kołodziej

Institutions: Rutgers, The State University of New Jersey, Jagiellonian University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W1482556154

FWCI: 13.31

Cites: 26

Cited by: 120

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