Regularity of the effective diffusivity of random diffusion with respect to anisotropy coefficient

Volume 189 / 2008

M. Cudna, T. Komorowski 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 $0$.

Authors

  • M. CudnaInstitute of Mathematics
    UMCS
    Pl. Marii Curie-Skłodowskiej 1
    20-031 Lublin, Poland
    e-mail
  • T. KomorowskiInstitute of Mathematics
    UMCS
    Pl. Marii Curie-Skłodowskiej 1
    20-031 Lublin, Poland
    and
    Institute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    e-mail

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