Hölder estimates near the boundary for quasilinear doubly degenerate parabolic equations

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 $\partial u/\partial t-\partial/\partial x_i\{a_0|u|^{\sigma(m-1)}|\nabla u|^{m-2}\partial u/\partial x_i\}=0$, $a_0>0$, $\sigma>0$, $m>2$.