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arXiv · 2410.20719

Uniform boundary Harnack principle for non-local operators on metric measure spaces

Shiping Cao·Zhen-Qing Chen
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Abstract

We obtain a uniform boundary Harnack principle (BHP) on any open sets for a large class of non-local operators on metric measure spaces under a jump measure comparability and tail estimate condition, and an upper bound condition on the distribution function for the exit times from balls. These conditions are satisfied by any non-local operator $\mathcal{L}$ that admits a two-sided mixed stable-like heat kernel bounds when the underlying metric measure spaces have volume doubling and reverse volume doubling properties. The results of this paper are new even for non-local operators on Euclidean spaces. In particular, our results give not only the scale invariant but also uniform BHP for the first time for non-local operators on Euclidean spaces of both divergence form and non-divergence form with measurable coefficients.

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Shiping Cao, Zhen-Qing Chen. 2024-10-28. Uniform boundary Harnack principle for non-local operators on metric measure spaces. https://arxiv.org/abs/2410.20719

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