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Abstract The Cauchy–Dirichlet and the Cauchy problem for the degenerate and singular quasilinear anisotropic parabolic equations are considered. We show that the time derivative u t of a solution u… Click to show full abstract
Abstract The Cauchy–Dirichlet and the Cauchy problem for the degenerate and singular quasilinear anisotropic parabolic equations are considered. We show that the time derivative u t of a solution u belongs to L ∞ under a suitable assumption on the smoothness of the initial data. Moreover, if the domain satisfies some additional geometric restrictions, then the spatial derivatives u x i belong to L ∞ as well. In the singular case we show that the second derivatives u x i x j of a solution of the Cauchy problem belong to L 2 .
Journal Title: Journal of Functional Analysis
Year Published: 2017
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