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arXiv · 2603.12065

Fractional $p$-caloric functions are Lipschitz

David Jesus·Aelson Sobral·José Miguel Urbano
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Abstract

We study the parabolic fractional $p-$Laplace equation $\partial_t u+(-\Delta_p)^su = 0$ in the degenerate range $2 < p < 2/(1-s)$. We show that weak solutions are Lipschitz continuous in space and, if $p > 1/(1-s)$, also in time. We also prove a comparison principle for both weak and viscosity solutions, and establish the equivalence between the two notions of solution.

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David Jesus, Aelson Sobral, José Miguel Urbano. 2026-03-12. Fractional $p$-caloric functions are Lipschitz. https://arxiv.org/abs/2603.12065

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