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arxiv: 2603.12065 · v2 · pith:OD2IDTXAnew · submitted 2026-03-12 · 🧮 math.AP

Fractional p-caloric functions are Lipschitz

David Jesus , Aelson Sobral , Jos\'e Miguel Urbano This is my paper
classification 🧮 math.AP
keywords fractionallipschitzsolutionsweakcaloriccomparisoncontinuousdegenerate
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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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  1. Lipschitz regularity for fractional $p$-Laplacian with coercive gradients

    math.AP 2026-04 unverdicted novelty 5.0

    Viscosity solutions to (-Δ_p)^s u + H(x, ∇u) = f are locally Lipschitz when p lies in (1, 2/(1-s)) ∪ (1, m+1), with Hölder subsolutions and only the zero bounded solution when f = 0 and H is x-independent.