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The Harnack inequality and related properties for solutions of elliptic and parabolic equations with divergence-free lower-order coefficients


Authors: A. I. Nazarov and N. N. Ural′tseva
Translated by: the authors
Original publication: Algebra i Analiz, tom 23 (2011), nomer 1.
Journal: St. Petersburg Math. J. 23 (2012), 93-115
MSC (2010): Primary 35B50, 35B53, 35B45
Published electronically: November 8, 2011
MathSciNet review: 2760150
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Abstract: The paper is devoted to the question as to how ``bad'' the junior coefficients of elliptic and parabolic equations may be in order that classical properties of their solutions (such as the strict maximum principle, the Harnack inequality and the Liouville theorem) still occur. The answers are given in terms of the Lebesgue and Morrey spaces.


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Additional Information

A. I. Nazarov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskaya Ul. 28, Stary Petergof, St. Petersburg 198504, Russia
Email: al.il.nazarov@gmail.com

N. N. Ural′tseva
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskaya Ul. 28, Stary Petergof, St. Petersburg 198504, Russia
Email: uunur@NU1253.spb.edu

DOI: https://doi.org/10.1090/S1061-0022-2011-01188-4
Keywords: Harnack inequality, Hölder estimates, maximum principle, Liouville theorem
Received by editor(s): October 12, 2010
Published electronically: November 8, 2011
Additional Notes: Partially supported by RFBR (grant no. 08-01-00748) and by grant NSh.4210.2010.1.
Dedicated: To the memory of Mikhail Solomonovich Birman
Article copyright: © Copyright 2011 American Mathematical Society