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

Nazarov, A.; Ural′tseva, N.

doi:10.1090/S1061-0022-2011-01188-4

The Harnack inequality and related properties for solutions of elliptic and parabolic equations with divergence-free lower-order coefficients
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by A. I. Nazarov and N. N. Ural′tseva
Translated by: the authors

St. Petersburg Math. J. 23 (2012), 93-115

DOI: https://doi.org/10.1090/S1061-0022-2011-01188-4

Published electronically: November 8, 2011

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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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