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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Boundary behavior of positive solutions of the heat equation on a semi-infinite slab


Author: B. A. Mair
Journal: Trans. Amer. Math. Soc. 295 (1986), 687-697
MSC: Primary 35K20; Secondary 31B25
MathSciNet review: 833703
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Abstract: In this paper, the abstract Fatou-Naim-Doob theorem is used to investigate the boundary behavior of positive solutions of the heat equation on the semi-infinite slab $ X = {{\mathbf{R}}^{n - 1}} \times {{\mathbf{R}}_ + } \times (0,T)$. The concept of semifine limit is introduced, and relationships are obtained between fine, semifine, parabolic, one-sided parabolic and two-sided parabolic limits at points on the parabolic boundary of $ X$. A Carleson-Calderón-type local Fatou theorem is also obtained for solutions on a union of two-sided parabolic regions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0833703-2
PII: S 0002-9947(1986)0833703-2
Keywords: Fine limit, semifine limit, parabolic limit, two-sided parabolic limit
Article copyright: © Copyright 1986 American Mathematical Society