Supremum estimates for parabolic stochastic partial differential equations

Marta Leocata (1) , Julien Vovelle (2)

1 SNS - Scuola Normale Superiore di Pisa
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We generalize the approach à la De Giorgi developed in [HsuWangWang2017] to get some estimates on the moments of the sup-norm of the solutions to parabolic stochastic partial differential equations. We also provide an alternative method, based on duality and estimates $L^1-L^r$ \`a la Boccardo-Gallou\"et [BoccardoGallouet89], for a backward stochastic partial differential equation.

Domaines: Mathématiques [math]

Marta Leocata, Julien Vovelle. Supremum estimates for parabolic stochastic partial differential equations. 2023. ⟨hal-04283613⟩