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Hölder estimates near the boundary for generalized solutions of quasilinear parabolic equations admitting double degeneration. (Russian. English summary) Zbl 0755.35058

Summary: Hölder estimates near the parabolic boundary of the cylinder \(Q_ T=\Omega\times(0,T]\) for weak solutions of quasilinear doubly degenerate parabolic equations is established. The typical example of an admissible equation is the equation of nonneutronian polytrophic filtration \[ \partial u/\partial t-\partial/\partial x_ i\{a_ 0| u|^{\sigma(m-1)}|\nabla u|^{m-2}\partial u/\partial x_ i\}=0,\quad a_ 0>0,\;\sigma>0,\;m>2. \]

MSC:

35K65 Degenerate parabolic equations
35D99 Generalized solutions to partial differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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