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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

   
 

 

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


Author: M. D. Surnachëv
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 75 (2014), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2014, 259-280
MSC (2010): Primary 35K92; Secondary 35K65
Published electronically: November 5, 2014
MathSciNet review: 3308612
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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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Additional Information

M. D. Surnachëv
Affiliation: Keldysh Institute of Applied Mathematics, Moscow
Email: peitsche@yandex.ru

DOI: https://doi.org/10.1090/S0077-1554-2014-00237-5
Keywords: Nonlinear parabolic equations, admissible weights, regularity of solutions, double degeneration, Muckenhoupt classes, Harnack inequality
Published electronically: November 5, 2014
Additional Notes: This research was supported by the Russian Foundation for Basic Research (grants No. 12-01-00058-a and 14-01-31341).
Dedicated: Dedicated to the centenary of the great mathematician Boris Moiseevich Levitan
Article copyright: © Copyright 2014 M. D. Surnachëv