A comparison principle for parabolic complex Monge-Amp\`ere equations
Complex Variables
2021-10-08 v2
Abstract
In this paper, we study the Cauchy-Dirichlet problem for Parabolic complex Monge-Amp\`ere equations on strongly pseudoconvex domains using the viscosity method. We prove a comparison principle for Parabolic complex Monge-Amp\`ere equations and use it to study the existence and uniqueness of viscosity solution in certain cases where the sets may be pairwise disjoint.
Keywords
Cite
@article{arxiv.2106.03311,
title = {A comparison principle for parabolic complex Monge-Amp\`ere equations},
author = {Hoang-Son Do and Thanh Cong Ngoc Pham},
journal= {arXiv preprint arXiv:2106.03311},
year = {2021}
}
Comments
15 pages. In the first version, there is an error in the proof of Lemma 3.3. In the second version, we add some conditions on $\Phi$ and $f$ under which our method works