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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
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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