Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise

TL;DR

This paper investigates the spatial and temporal regularity properties of solutions to a class of stochastic partial differential equations driven by nonlinear multiplicative trace class noise, providing insights into their behavior.

Contribution

It offers a novel analysis of regularity for SPDEs with nonlinear multiplicative trace class noise, expanding understanding beyond linear cases.

Findings

Established regularity results for solutions in space and time

Identified conditions for solution smoothness

Extended existing theory to nonlinear multiplicative noise

Abstract

In this article spatial and temporal regularity of the solution process of a stochastic partial differential equation (SPDE) of evolutionary type with nonlinear multiplicative trace class noise is analyzed.