Regularity up to the boundary for generalized solutions to the first boundary-value problem for doubly degenerate quasilinear parabolic equations

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For quasilinear doubly degenerate parabolic equations it has been possible to establish the existence of nonnegative generalized solutions to the first boundary-value problem that are Holder continuous up to the boundary of the cylinder QT=Ωx(0, T]. A typical example of an admissible equation is the equation of Newtonian polytropic filtration $$\frac{{\partial u}}{{\partial t}} - \frac{\partial }{{\partial x_i }}\left\{ {a_0 \left| u \right|^l \left| {u_x } \right|^{m - 2} u_{x_i } } \right\} = 0, a_0 > 0,l > 0,m > 2.$$ .