On the regularity of the complex Hessian equation-Reference-Cited by-同舟云学术

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On the regularity of the complex Hessian equation

Published:2022-06-30 Issue: Volume: Page:
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Åhag Per,Czyż Rafał

Abstract

This note aims to investigate the regularity of a solution to the Dirichlet problem for the complex Hessian equation, which has a density of the m m -Hessian measure that belongs to L q L^q , for q ≤ n m q\leq \frac nm .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/0000-000-00/S0002-9939-2022-16042-0/S0002-9939-2022-16042-0.pdf

Reference28 articles.

1. Potential theory in the class of 𝑚-subharmonic functions;Sadullaev, A.;Tr. Mat. Inst. Steklova,2012

2. Capacities and Hessians in the class of 𝑚-subharmonic functions;Sadullaev, A.;Dokl. Akad. Nauk,2013

3. The geometry of 𝑚-hyperconvex domains;Åhag, Per;J. Geom. Anal.,2018

4. Poincaré- and Sobolev- type inequalities for complex 𝑚-Hessian equations;Åhag, Per;Results Math.,2020

5. Per Åhag and Rafał Czyż, A characterization of the degenerate complex Hessian equations for functions with bounded (𝑝,𝑚)-energy, Ann. Sc. Norm. Super. Pisa Cl. Sci., to appear, arXiv:2003.06157, 2020, DOI 10.2422/2036-2145.202105_017.

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