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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Harnack-type inequalities for evolution equations


Authors: Giles Auchmuty and David Bao
Journal: Proc. Amer. Math. Soc. 122 (1994), 117-129
MSC: Primary 35K22; Secondary 35B45, 35Q40
DOI: https://doi.org/10.1090/S0002-9939-1994-1219716-X
MathSciNet review: 1219716
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Abstract: Here we derive Harnack inequalities for nonnegative solutions of the porous medium equation and the p-diffusion equation. The method applies to functions obeying certain a priori evolution inequalities. The proofs are based on optimizing inequalities for the convective derivative of the function along a path.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1219716-X
Article copyright: © Copyright 1994 American Mathematical Society