Local Hölder regularity for nonlocal parabolic \(p\)-Laplace equations

We prove local H\"older regularity for a nonlocal parabolic equations of the form \begin{align*} \partial_t u + \text{P.V.}\int_{\mathbb{R}^N} \frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+sp}}\,dy=0, \end{align*} for \(p\in (1,\infty)\) and \(s \in (0,1)\).

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Published in:arXiv.org 2024-01
Main Authors: Adimurthi, Karthik, Prasad, Harsh, Tewary, Vivek
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Language:English
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Laplace equation
Mathematical analysis
Regularity
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Prasad, Harsh
Tewary, Vivek
description We prove local H\"older regularity for a nonlocal parabolic equations of the form \begin{align*} \partial_t u + \text{P.V.}\int_{\mathbb{R}^N} \frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+sp}}\,dy=0, \end{align*} for \(p\in (1,\infty)\) and \(s \in (0,1)\).
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subjects Laplace equation
Mathematical analysis
Regularity
title Local Hölder regularity for nonlocal parabolic \(p\)-Laplace equations
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