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