Regularity of the effective diffusivity of random diffusion with respect to anisotropy coefficient
Volume 189 / 2008
Studia Mathematica 189 (2008), 269-286
MSC: Primary 60F17, 35B27; Secondary 60G44.
DOI: 10.4064/sm189-3-5
Abstract
We show that the effective diffusivity of a random diffusion with a drift is a continuous function of the drift coefficient. In fact, in the case of a homogeneous and isotropic random environment the function is $C^\infty $ smooth outside the origin. We provide a one-dimensional example which shows that the diffusivity coefficient need not be differentiable at $0$.
