Fractional p-caloric functions are Lipschitz (Preprint)

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Type: Preprint
National /International: International
Title: Fractional p-caloric functions are Lipschitz
Publication Date: 2026-03-12
Authors: - David Jesus
- Aelson Sobral
- José Miguel Urbano
Abstract:

We study the parabolic fractional \( p \)-Laplace equation \( \partial_t u+(-\Delta_p)^su = 0 \) in the degenerate range \( 2 \leq p < 2/(1-s) \). 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.

Institution: arXiv:2603.12065
Online version: https://arxiv.org/abs/2603.12065
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