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Estimates on the Fundamental Solution to Heat Flows With Uniformly Elliptic Coefficients
Author(s) -
Norris James R.,
Stroock Daniel W.
Publication year - 1991
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-62.2.373
Subject(s) - mathematics , mathematical analysis , elliptic partial differential equation , initial value problem , cauchy distribution , partial differential equation
We obtain estimates, from above and below, on the fundamental solution to the Cauchy initial value problem for parabolic equations having uniformly elliptic coefficients. We impose minimal regularity requirements on the coefficients. The estimates are expressed in terms of an energy functional associated with the coefficients.