Title: Improved regularity for the stochastic fast diffusion equation Show Chinese title

Title: 随机快速扩散方程的改进正则性

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 $L^{2}$. Show Chinese abstract

Abstract: 我们证明了带有参数$m\in (0,1)$的奇异退化随机快速扩散方程，在任意空间维数中有界区域上的零狄利克雷边界条件，并由线性乘法维纳噪声驱动，其解在 Sobolev 空间$W^{1,m+1}_0$中表现出改进的正则性，对于初始数据在$L^{2}$中的情况。