Supremum estimates for degenerate, quasilinear stochastic partial differential equations
- Authors: Konstantinos Dareiotis, Benjamin Gess
- Preprint year: 2017
- First public date: 2017-12-18
- arXiv: 1712.06655
- Status: Published
- Publication type: Journal article
- Publication year: 2019
- Journal: Annales de l'Institut Henri Poincaré / B : Probabilites et statistiques, 55 (2019) 3, pp. 1765-1796
- DOI: 10.1214/18-AIHP934
Abstract
We prove a priori estimates in $L_\infty$ for a class of quasilinear stochastic partial differential equations. The estimates are obtained independently of the ellipticity constant $arepsilon$ and thus imply analogous estimates for degenerate quasilinear stochastic partial differential equations, such as the stochastic porous medium equation.