Bounded weak solutions to parabolic p-Laplace systems with Hölder continuous coefficients have locally Hölder continuous spatial gradients for every p > 1, with quantitative estimates in terms of the solution's oscillation.
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Schauder estimates for parabolic $p$-Laplace systems
Bounded weak solutions to parabolic p-Laplace systems with Hölder continuous coefficients have locally Hölder continuous spatial gradients for every p > 1, with quantitative estimates in terms of the solution's oscillation.