Moser-Trudinger inequalities and complex Monge-Ampere equation
Complex Variables
2023-08-01 v3 Analysis of PDEs
Abstract
Our aim is to give a version of the Moser-Trudinger inequality in the setting of complex geometry. As a very particular case, our result already gives a new Moser-Trudinger inequality for functions in the Sobolev space of a domain in . We also deduce a new necessary condition for the complex Monge-Ampere equation for a given measure on a compact Kahler manifold to admit a Holder continuous solution.
Cite
@article{arxiv.2006.07979,
title = {Moser-Trudinger inequalities and complex Monge-Ampere equation},
author = {Tien-Cuong Dinh and George Marinescu and Duc-Viet Vu},
journal= {arXiv preprint arXiv:2006.07979},
year = {2023}
}
Comments
Final version, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)