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

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

2010-11-08

arxiv.org/abs/1011.1888v1

Mathematics

Analysis of PDEs

Scientific paper

We discuss the problem how "bad" may be lower-order coefficients in elliptic
and parabolic second order equations to ensure some qualitative properties of
solution such as strong maximum principle, Harnack's inequality, Liouville's
theorem. The answers are given in terms of the Lebesgue spaces and the Morrey
spaces.

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