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

M. D. Surnachëv
2014 Transactions of the Moscow Mathematical Society  
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. 2010
more » ... linear case. 2010 Mathematics Subject Classification. Primary 35K92; Secondary 35K65.
doi:10.1090/s0077-1554-2014-00237-5 fatcat:sp4yqamksvf33hzmhpjstqr354