Fatou theorems for parabolic equations

Author:
Caroline Sweezy

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2343-2355

MSC (1991):
Primary 35K20, 42K25

DOI:
https://doi.org/10.1090/S0002-9939-96-03687-8

MathSciNet review:
1363188

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Abstract: For elliptic parabolic operators with time dependent coefficients, bounded and measurable, the absolute continuity of the two caloric measures plus a Fatou theorem are shown to hold on the parabolic boundary of a smooth cylinder given a Carleson-type condition on the coefficients of the operators, and assuming one of the measures is a center doubling measure. Given a stronger Carleson condition, and no doubling assumption, another kind of Fatou theorem result holds. The method of proof follows that of Fefferman, Kenig and Pipher.

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Additional Information

**Caroline Sweezy**

Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003

Email:
csweezy@nmsu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03687-8

Received by editor(s):
May 18, 1994

Received by editor(s) in revised form:
December 7, 1994

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1996
American Mathematical Society