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A Comparison Principle for Parabolic Complex Monge–Ampère Equations

The Journal of Geometric Analysis volume 32, Article number: 6 (2022) Cite this article

Abstract

In this paper, we study the Cauchy–Dirichlet problem for parabolic complex Monge–Ampère equations on strongly pseudoconvex domains using the viscosity method. We prove a comparison principle for parabolic complex Monge–Ampère 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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Acknowledgements

The second-named author would like to thank Vingroup Innovation Foundation (VINIF) for supporting his Master studies at VNU University of Science, Hanoi.

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Authors and Affiliations

  1. Institute of Mathematics Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Hoang-Son Do

  2. Department of Mathematics, VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Ha Noi, Vietnam

    Thanh Cong Ngoc Pham

Authors
  1. Hoang-Son Do
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  2. Thanh Cong Ngoc Pham
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Correspondence to Hoang-Son Do.

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Dedicated to Professor Ahmed Zeriahi on the occasion of his retirement. The first author was supported by Vietnam Academy of Science and Technology under Grant Number CT0000.07/21-22.

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Do, HS., Pham, T.C.N. A Comparison Principle for Parabolic Complex Monge–Ampère Equations. J Geom Anal 32, 6 (2022). https://doi.org/10.1007/s12220-021-00748-4

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  • DOI: https://doi.org/10.1007/s12220-021-00748-4

Keywords

  • Viscosity solutions
  • Parabolic Monge–Ampère equation
  • Pluripotential theory

Mathematics Subject Classification

  • 32W20
  • 32U15
  • 35K10
  • 35D40