Geodesic
Regularity of the effective diffusivity of random diffusion with respect to anisotropy coefficient
M. Cudna 1   ; T. Komorowski 2
1 Institute of Mathematics UMCS Pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland
2 Institute 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
Studia Mathematica, Tome 189 (2008) no. 3, pp. 269-286 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $0$.
DOI : 10.4064/sm189-3-5
Keywords: effective diffusivity random diffusion drift continuous function drift coefficient homogeneous isotropic random environment function infty smooth outside origin provide one dimensional example which shows diffusivity coefficient differentiable

M. Cudna  1   ; T. Komorowski  2

1 Institute of Mathematics UMCS Pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland
2 Institute 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 
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     title = {Regularity of the effective diffusivity of random diffusion
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M. Cudna; T. Komorowski. Regularity of the effective diffusivity of random diffusion
 with respect to anisotropy coefficient. Studia Mathematica, Tome 189 (2008) no. 3, pp. 269-286. doi: 10.4064/sm189-3-5

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