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Hölder gradient estimates for a class of singular or degenerate parabolic equations

Abstract : We prove interior Hölder estimate for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic equation u t = |∇u| κ div(|∇u|^{ p−2} ∇u), where p ∈ (1, ∞) and κ ∈ (1 − p, ∞). This includes the from L^∞ to C^{1,α} regularity for parabolic p-Laplacian equations in both divergence form with κ = 0, and non-divergence form with κ = 2 − p. This work is a continuation of a paper by the last two authors [12].
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Cyril Imbert, Tianling Jin, Luis Silvestre. Hölder gradient estimates for a class of singular or degenerate parabolic equations. Advances in Nonlinear Analysis, De Gruyter, 2019, 8 (1), pp.845-867. ⟨10.1515/anona-2016-0197⟩. ⟨hal-01360547⟩

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