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arXiv · 2205.10111

H\"older regularity for parabolic fractional $p$-Laplacian

Naian Liao
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Abstract

Local H\"older regularity is established for certain weak solutions to a class of parabolic fractional $p$-Laplace equations with merely measurable kernels. The proof uses DeGiorgi's iteration and refines DiBenedetto's intrinsic scaling method. The control of a nonlocal integral of solutions in the reduction of oscillation plays a crucial role and entails delicate analysis in this intrinsic scaling scenario. Dispensing with any logarithmic estimate and any comparison principle, the proof is new even for the linear case.

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Naian Liao. 2022-05-20. H\"older regularity for parabolic fractional $p$-Laplacian. https://arxiv.org/abs/2205.10111

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