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Hölder estimates for local solutions of some doubly nonlinear degenerate parabolic equations. (English) Zbl 0796.35089
The authors consider quasilinear parabolic equations with principal part in divergence form of the type $$u\sb t - \text{div} a(x,t,u,Du) = b(x,t,u,Du)$$ in ${\cal D}' (\Omega\sb T)$ where $\Omega$ is a bounded open set in $\bbfR\sp N$, $0<T<\infty$, $\Omega\sb T = \Omega \times (0,T)$; here the functions $a$ and $b$ are assumed to be measurable and to satisfy several further (structure) conditions. Utilizing and generalizing results of O. A. Ladyzhenskaya, N. A. Solonnikov and N. N. Ural’tzeva as well as of E. Di Benedetto, the authors establish interior and boundary Hölder estimates for bounded weak solutions, e.g., for suitable Dirichlet and Neumann problems. [For related investigations, cf. also papers by {\it A. V. Ivanov} of the last five years, e.g., Algebra Anal. 3, No. 2, 139-179 (1991; Zbl 0764.35026)].

35K65Parabolic equations of degenerate type
35D10Regularity of generalized solutions of PDE (MSC2000)
35K60Nonlinear initial value problems for linear parabolic equations
35K55Nonlinear parabolic equations
35B45A priori estimates for solutions of PDE
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