Green's Functions for Elliptic and Parabolic Equations with Random Coeecients
نویسندگان
چکیده
This paper is concerned with linear uniformly elliptic and par abolic partial di erential equations in divergence form It is assumed that the coe cients 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 par ticular it is shown that the expectation value is a continuously di erentiable function whose derivatives are bounded by the corresponding derivatives of the heat equation Similar results are obtained for the related nite di erence equations
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Green's Functions for Elliptic and Parabolic Equations with Random Coefficients Ii
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