Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 3

Special Issue in Honor of Duong H. Phong

Edited by Tristan Collins, Valentino Tosatti, and Ben Weinkove

Pluripotential solutions versus viscosity solutions to complex Monge–Ampère flows

Pages: 971 – 990

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n3.a5

Authors

Vincent Guedj (Institut de Mathématiques de Toulouse, Université de Toulouse, France)

Chinh H. Lu (Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay, Orsay, France)

Ahmed Zeriahi (Institut de Mathématiques de Toulouse, Université de Toulouse, France)

Abstract

We compare various notions of weak subsolutions to degenerate complex Monge–Ampère flows, showing that they all coincide. This allows us to show that the viscosity solution coincides with the envelope of pluripotential subsolutions.

Keywords

parabolic Monge–Ampère equation, pluripotential solution, viscosity solution, Perron envelope

2010 Mathematics Subject Classification

Primary 32W20, 53C44. Secondary 58J35.

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The authors are partially supported by the ANR project GRACK.

Received 6 April 2019

Accepted 15 September 2019

Published 14 June 2021