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

By Alexander I. Nazarov, N. N. Ural'tseva. 2010

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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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8afe1875ff765ddc57179baaa8dce1fa4044dc5c