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arXiv · 2603.21121

Weak Harnack inequality and Cartan property for nonlocal $W^{s,1}$-minimizers

Panu Lahti·Yuxin Li·Khanh Nguyen
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Abstract

We establish a weak Harnack inequality for nonlocal $W^{s,1}$-subminimizers in a complete, connected, doubling metric measure space where $0<s<1$. As a corollary, we prove that $W^{s,1}$-subminimizers are semicontinuous, up to a suitable choice of pointwise representative. We then prove \emph{Cartan-type properties} for $W^{s,1}$-superminimizers. The theory turns out to be mostly analogous with the local case of BV super- and subminimizers. Our results seem to be new even in the classical Euclidean setting.

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Panu Lahti, Yuxin Li, Khanh Nguyen. 2026-03-22. Weak Harnack inequality and Cartan property for nonlocal $W^{s,1}$-minimizers. https://arxiv.org/abs/2603.21121

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