Geodesic
H\"older estimates near the boundary for quasilinear doubly degenerate parabolic equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 22, Tome 188 (1991), pp. 45-69

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Hölder estimates near the parabolic boundary of cylinder $Q_T=\Omega\times(0,T]$ for weak solutions of quasilinear doubly degenerate parabolic equations is established. The typical example of admissible equation is the equation of nonneutonian polythropic filtration $\partial u/\partial t-\partial/\partial x_i\{a_0|u|^{\sigma(m-1)}|\nabla u|^{m-2}\partial u/\partial x_i\}=0$, $a_0>0$, $\sigma>0$, $m>2$. 
@article{ZNSL_1991_188_a1,
     author = {A. V. Ivanov},
     title = {H\"older estimates near the boundary for quasilinear doubly degenerate parabolic equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {45--69},
     publisher = {mathdoc},
     volume = {188},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_188_a1/}
}
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A. V. Ivanov. H\"older estimates near the boundary for quasilinear doubly degenerate parabolic equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 22, Tome 188 (1991), pp. 45-69. http://geodesic.mathdoc.fr/item/ZNSL_1991_188_a1/