TY - JOUR
T1 - Improved regularity for the stochastic fast diffusion equation
AU - Ciotir, Ioana
AU - Goreac, Dan
AU - Tölle, Jonas M.
PY - 2024/2/23
Y1 - 2024/2/23
N2 - 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 $L^{2}$.
AB - 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 $L^{2}$.
KW - Stochastic singular-degenerate diffusion equation
KW - stochastic partial differential equation
KW - stochastic fast diffusion equation
KW - improved Sobolev regularity
KW - linear multiplicative Wiener noise
M3 - Article
SN - 1083-589X
VL - 29
SP - 1
EP - 7
JO - Electronic Communications in Probability
JF - Electronic Communications in Probability
M1 - 5
ER -