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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Green’s functions for elliptic and parabolic equations with random coefficients II
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by Joseph G. Conlon PDF
Trans. Amer. Math. Soc. 356 (2004), 4085-4142 Request permission


This paper is concerned with linear parabolic partial differential equations in divergence form and their discrete analogues. It is assumed that the coefficients of the equation are stationary random variables, random in both space and 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 in the space variable whose derivatives are bounded by the corresponding derivatives of the Green’s function for the heat equation. Similar results are obtained for the related finite difference equations. This paper generalises results of a previous paper which considered the case when the coefficients are constant in time but random in space.
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Additional Information
  • Joseph G. Conlon
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
  • Email:
  • Received by editor(s): July 23, 2002
  • Received by editor(s) in revised form: July 15, 2003
  • Published electronically: January 16, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 4085-4142
  • MSC (2000): Primary 81T08, 82B20, 35R60, 60J75
  • DOI:
  • MathSciNet review: 2058840