Viscosity solutions to parabolic complex Monge-Ampère equations

Hoang-Son Do (1) , Giang Le , Tat Dat Tô (2)

1 VAST - Vietnam Academy of Science and Technology
2 ENAC - Ecole Nationale de l'Aviation Civile

In this paper, we study the Cauchy-Dirichlet problem for Parabolic complex Monge-Amp\`ere equations on a strongly pseudoconvex domain by the viscosity method. We extend the results in [EGZ15b] on the existence of solution and the convergence at infinity. We also establish the H\"older regularity of the solutions when the Cauchy-Dirichlet data are H\"older continuous.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Variables complexes [math.CV]

Hoang-Son Do, Giang Le, Tat Dat Tô. Viscosity solutions to parabolic complex Monge-Ampère equations. Calculus of Variations and Partial Differential Equations, 2020, 59 (45 (2020)), ⟨10.1007/s00526-020-1700-3⟩. ⟨hal-02370331⟩