Supremum estimates for degenerate, quasilinear stochastic partial differential equations

TL;DR

This paper establishes supremum estimates for a class of degenerate, quasilinear stochastic PDEs, providing bounds that are independent of ellipticity, with applications to equations like the stochastic porous medium equation.

Contribution

It introduces a priori $L_ abla$ estimates for degenerate quasilinear stochastic PDEs that do not depend on the ellipticity constant, extending the analysis to degenerate cases.

Findings

Supremum estimates are obtained independently of the ellipticity constant.

The results apply to degenerate equations like the stochastic porous medium equation.

Provides a framework for analyzing degenerate stochastic PDEs.

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 $\varepsilon$ and thus imply analogous estimates for degenerate quasilinear stochastic partial differential equations, such as the stochastic porous medium equation.