Geodesic
Regularity of solutions of parabolic equations with a double nonlinearity and a weight
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 75 (2014) no. 2, pp. 309-334

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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. 
@article{MMO_2014_75_2_a10,
     author = {M. D. Surnach\"ev},
     title = {Regularity of solutions of parabolic equations with a double nonlinearity and a weight},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {309--334},
     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a10/}
}
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M. D. Surnachëv. Regularity of solutions of parabolic equations with a double nonlinearity and a weight. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 75 (2014) no. 2, pp. 309-334. http://geodesic.mathdoc.fr/item/MMO_2014_75_2_a10/