Pure and Applied Mathematics Quarterly
Volume 17 (2021)
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
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.
parabolic Monge–Ampère equation, pluripotential solution, viscosity solution, Perron envelope
2010 Mathematics Subject Classification
Primary 32W20, 53C44. Secondary 58J35.
The authors are partially supported by the ANR project GRACK.
Received 6 April 2019
Accepted 15 September 2019
Published 14 June 2021