Hölder estimates for solutions of degenerate nondivergence elliptic and parabolic equations

Author:
A. I. Nazarov

Translated by:
the author

Original publication:
Algebra i Analiz, tom **21** (2009), nomer 4.

Journal:
St. Petersburg Math. J. **21** (2010), 635-650

MSC (2010):
Primary 35B45; Secondary 35J70, 35K65

Published electronically:
May 20, 2010

MathSciNet review:
2584211

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We deal with a class of nondivergence type elliptic and parabolic equations degenerating at the coordinate hyperplanes. Assuming that the degeneration is coordinatewise and varies regularly, we prove the Hölder continuity of solutions. Also, the approximative solutions are considered.

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Additional Information

**A. I. Nazarov**

Affiliation:
Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Petrodvorets, St. Petersburg 198504, Russia

Email:
al.il.nazarov@gmail.com

DOI:
http://dx.doi.org/10.1090/S1061-0022-2010-01109-9

Keywords:
Nondivergence equations,
H\"older estimates,
degeneration,
regularly varying functions

Received by editor(s):
September 8, 2008

Published electronically:
May 20, 2010

Additional Notes:
The paper is supported by the grant NSh.227.2008.1 and by RFBR grant 08-01-00748

Dedicated:
To my teacher Nina Nikolaevna Ural′tseva on the occasion of her birthday.

Article copyright:
© Copyright 2010
American Mathematical Society