Pure-measure-theory De Giorgi-type estimates yield local boundedness, weak Harnack, Harnack, Hölder, and Liouville results for nonlocal parabolic energy classes, with a comparison-principle-free Harnack proof.
Local H\"older regularity for nonlocal parabolic $p$-Laplace equations
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abstract
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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2025 1verdicts
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Nonlocal parabolic De Giorgi classes
Pure-measure-theory De Giorgi-type estimates yield local boundedness, weak Harnack, Harnack, Hölder, and Liouville results for nonlocal parabolic energy classes, with a comparison-principle-free Harnack proof.