Improved regularity for the stochastic fast diffusion equation

TL;DR

This paper proves that solutions to a stochastic fast diffusion equation with singular degeneracy and multiplicative noise gain improved Sobolev regularity, enhancing understanding of their smoothness properties.

Contribution

It establishes new regularity results for solutions of the stochastic fast diffusion equation with zero boundary conditions and multiplicative noise, extending previous deterministic findings.

Findings

Solutions exhibit improved regularity in Sobolev space $W^{1,m+1}_0$

Regularity holds for initial data in $L^{2}$

Results apply in any spatial dimension

Abstract

We prove that the solution to the singular-degenerate stochastic fast-diffusion equation with parameter $m\in (0,1)$, with zero Dirichlet boundary conditions on a bounded domain in any spatial dimension, and driven by linear multiplicative Wiener noise, exhibits improved regularity in the Sobolev space $W^{1,m+1}_0$ for initial data in $L^{2}$.