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

Full-text PDF

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 which vanish on , where is a bounded Lipschitz domain in . This inequality is applied to the proof of the Hölder continuity of the quotient of two positive solutions vanishing on a portion of

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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