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Zbl 0796.35089
Porzio, M.M.; Vespri, V.
Hölder estimates for local solutions of some doubly nonlinear degenerate parabolic equations. (English)
[J] J. Differ. Equations 103, No.1, 146-178 (1993). ISSN 0022-0396

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)].
[M.Kracht (Düsseldorf)]

MSC 2000:: *35K65 Parabolic equations of degenerate type
35D10 Regularity of generalized solutions of PDE
35K60 (Nonlinear) BVP for (non)linear parabolic equations
35K55 Nonlinear parabolic equations
35B45 A priori estimates

Keywords: quasilinear parabolic equations; interior and boundary Hölder estimates; Dirichlet and Neumann problems

Citations: Zbl 0764.35026

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