Behavior near the boundary of positive solutions of second order parabolic equations. II
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- by E. B. Fabes, M. V. Safonov and Yu Yuan
- Trans. Amer. Math. Soc. 351 (1999), 4947-4961
- DOI: https://doi.org/10.1090/S0002-9947-99-02487-3
- Published electronically: August 10, 1999
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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 $\partial _xQ.$References
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Bibliographic 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
- 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1665328