Regularity of solutions of parabolic equations with a double nonlinearity and a weight

Surnachëv, M.

doi:10.1090/S0077-1554-2014-00237-5

Regularity of solutions of parabolic equations with a double nonlinearity and a weight
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by M. D. Surnachëv
Translated by: E. Khukhro

Trans. Moscow Math. Soc. 2014, 259-280

DOI: https://doi.org/10.1090/S0077-1554-2014-00237-5

Published electronically: November 5, 2014

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Abstract:

We study local regularity of solutions of nonlinear parabolic equations with a double degeneracy and a weight. We impose the condition of $p$-admissibility on the weight; in particular this allows weights in the Muckenhoupt classes $A_p$. We prove that solutions are locally Hölderian without any restriction on the sign being constant. We prove a Harnack inequality for nonnegative solutions. We examine the stability of the constants as the parameters in the equation approach the linear case

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