Pluripotential solutions versus viscosity solutions to complex Monge-Ampère flows

Vincent Guedj (1) , Chinh H. Lu (2) , Ahmed Zeriahi (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LMO - Laboratoire de Mathématiques d'Orsay

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. Dedicated to Duong Hong Phong on the occasion of his 65th birthday.

Mots clés: Parabolic Pluripotential Theory; Complex Monge-Amp\`ere flows; Viscosity solutions.

Domaines: Variables complexes [math.CV]; Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]

Vincent Guedj, Chinh H. Lu, Ahmed Zeriahi. Pluripotential solutions versus viscosity solutions to complex Monge-Ampère flows. 2019. ⟨hal-02288829⟩