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Fatou theorems for parabolic equations

Author: Caroline Sweezy
Journal: Proc. Amer. Math. Soc. 124 (1996), 2343-2355
MSC (1991): Primary 35K20, 42K25
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

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