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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fatou theorems for parabolic equations
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by Caroline Sweezy
Proc. Amer. Math. Soc. 124 (1996), 2343-2355
DOI: https://doi.org/10.1090/S0002-9939-96-03687-8

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.
References
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Bibliographic Information
  • Caroline Sweezy
  • Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
  • Email: csweezy@nmsu.edu
  • Received by editor(s): May 18, 1994
  • Received by editor(s) in revised form: December 7, 1994
  • Communicated by: J. Marshall Ash
  • © Copyright 1996 American Mathematical Society
  • 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