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Published: 
September 15, 2000

Keywords: 
Green's functions, diffusions, random environments

Subject: 
35R60, 60J75

Abstract:

This paper is concerned with linear uniformly elliptic and parabolic partial
differential equations in divergence form. It is assumed that the coefficients
of the equations are random variables, constant in time. The Green's functions
for the equations are then random variables. Regularity properties for
expectation values of Green's functions are obtained. In particular, it is
shown that the expectation value is a continuously differentiable function
whose derivatives are bounded by the corresponding derivatives of the heat
equation. Similar results are obtained for the related finite difference
equations.

Author information:
Joseph G. Conlon :
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109
conlon@math.lsa.umich.edu
http://www.math.lsa.umich.edu/~conlon/
Ali Naddaf :
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109
naddaf@math.lsa.umich.edu
 