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arXiv · 1911.05619

The Harnack inequality for a class of nonlocal parabolic equations

Agnid Banerjee·Nicola Garofalo·Isidro H. Munive·Duy-Minh Nhieu
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Abstract

In this paper we establish a scale invariant Harnack inequality for the fractional powers of parabolic operators $(\partial_t - \mathscr{L})^s$, $0<s<1$, where $\mathscr{L}$ is the infinitesimal generator of a class of symmetric semigroups. As a by-product we also obtain a similar result for the nonlocal operators $(-\mathscr{L})^s$. Our focus is on non-Euclidean situations.

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Agnid Banerjee, Nicola Garofalo, Isidro H. Munive, Duy-Minh Nhieu. 2019-11-13. The Harnack inequality for a class of nonlocal parabolic equations. https://arxiv.org/abs/1911.05619

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