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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Behavior near the boundary
of positive solutions
of second order parabolic equations. II


Authors: E. B. Fabes, M. V. Safonov and Yu Yuan
Journal: Trans. Amer. Math. Soc. 351 (1999), 4947-4961
MSC (1991): Primary 35K10, 35B05; Secondary 35B45, 31B25
DOI: https://doi.org/10.1090/S0002-9947-99-02487-3
Published electronically: August 10, 1999
MathSciNet review: 1665328
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Abstract | References | Similar Articles | Additional Information

Abstract: A boundary backward Harnack inequality is proved for positive solutions of second order parabolic equations in non-divergence form in a bounded cylinder $Q=\Omega \times \left(0,T\right)$ which vanish on $\partial _xQ=\partial\Omega\times \left(0,T\right)$, where $\Omega$ is a bounded Lipschitz domain in $\mathbb{R}^n$. This inequality is applied to the proof of the Hölder continuity of the quotient of two positive solutions vanishing on a portion of $\partial _xQ.$


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Additional Information

M. V. Safonov
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455-0100
Email: safonov@math.umn.edu

Yu Yuan
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455-0100
Address at time of publication: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email: yyuan@math.utexas.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02487-3
Keywords: Harnack inequality, H\"{o}lder continuity, caloric measure.
Received by editor(s): August 4, 1997
Published electronically: August 10, 1999
Additional Notes: The second and third authors are partially supported by NSF Grant No. DMS-9623287
Article copyright: © Copyright 1999 American Mathematical Society