Quasi-linear Stochastic Partial Differential Equations with irregular Coefficients - Malliavin regularity of the Solutions

TL;DR

This paper investigates the Malliavin regularity of solutions to quasi-linear stochastic PDEs with irregular, discontinuous drift coefficients, establishing directional differentiability under minimal conditions.

Contribution

It demonstrates that solutions are directionally Malliavin differentiable even with bounded, measurable, and discontinuous drift coefficients.

Findings

Solutions are directionally Malliavin differentiable with irregular coefficients

Regularity results hold under minimal boundedness and measurability conditions

Advances understanding of stochastic PDEs with non-smooth drifts

Abstract

We study quasi-linear stochastic partial differential equations with discontinuous drift coefficients. Existence and uniqueness of a solution is already known under weaker conditions on the drift, but we are interested in the regularity of the solution in terms of Malliavin calculus. We prove that when the drift is bounded and measurable the solution is directional Malliavin differentiable.