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Trudy Moskovskogo Matematicheskogo Obshchestva, 2014, Volume 75, Issue 2, Pages 309–334
(Mi mmo568)
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This article is cited in 9 scientific papers (total in 9 papers)
Regularity of solutions of parabolic equations with a double nonlinearity and a weight
M. D. Surnachëv M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow
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.
Received: 31.03.2014
Citation:
M. D. Surnachëv, “Regularity of solutions of parabolic equations with a double nonlinearity and a weight”, Tr. Mosk. Mat. Obs., 75, no. 2, MCCME, M., 2014, 309–334; Trans. Moscow Math. Soc., 75 (2014), 259–280
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https://www.mathnet.ru/eng/mmo568 https://www.mathnet.ru/eng/mmo/v75/i2/p309
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Abstract page: | 332 | Full-text PDF : | 110 | References: | 56 |
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