Abstract
In this paper, we study the Cauchy–Dirichlet problem for Parabolic complex Monge–Ampère equations on a strongly pseudoconvex domain using the viscosity method. We extend the results in Eyssidieux et al. (Math Ann 362:931–963, 2015) on the existence of solution and the convergence at infinity. We also establish the Hölder regularity of the solutions when the Cauchy–Dirichlet data are Hölder continuous.
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Acknowledgements
The authors are grateful to Vincent Guedj and Ahmed Zeriahi for very useful discussions. This work was begun during a visit by the first-named author to the Institut de Mathématiques de Toulouse (from September 1 to September 30, 2018) funded by LIA Formath Vietnam and ANR GRACK. This paper was partially written while the first-named author visited Vietnam Institute for Advanced Study in Mathematics(VIASM). He would like to thank these institutions for their hospitality. The authors would like to thank the referee for very useful comments and suggestions.
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Communicated by N. Trudinger.
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The first-named author was funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2017.306.
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Do, HS., Le, G. & Tô, T.D. Viscosity solutions to parabolic complex Monge–Ampère equations. Calc. Var. 59, 45 (2020). https://doi.org/10.1007/s00526-020-1700-3
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DOI: https://doi.org/10.1007/s00526-020-1700-3