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arXiv · 2106.03311

A comparison principle for parabolic complex Monge-Amp\`ere equations

Hoang-Son Do·Thanh Cong Ngoc Pham
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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 $\{z\in\Omega: f(t, z)=0 \}$ may be pairwise disjoint.

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Hoang-Son Do, Thanh Cong Ngoc Pham. 2021-06-07. A comparison principle for parabolic complex Monge-Amp\`ere equations. https://arxiv.org/abs/2106.03311

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