English

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 {zΩ:f(t,z)=0}\{z\in\Omega: f(t, z)=0 \} 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

R2 v1 2026-06-24T02:53:40.099Z