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arXiv · 2401.04549

Riesz potential estimates for mixed local-nonlocal problems with measure data

Iwona Chlebicka·Kyeong Song·Yeonghun Youn·Anna Zatorska-Goldstein
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Abstract

We study gradient regularity for mixed local-nonlocal problems modelled upon \[ -\Delta_p u +(-\Delta_p)^su=\mu\qquad\text{for} \quad 2-\tfrac{1}{n}<p<\infty\quad \text{and}\quad s\in(0,1)\,,\] where $\mu$ is a bounded Borel measure. We prove pointwise bounds for the gradient $Du$ in terms of the truncated 1-Riesz potential of $\mu$.

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Iwona Chlebicka, Kyeong Song, Yeonghun Youn, Anna Zatorska-Goldstein. 2024-01-09. Riesz potential estimates for mixed local-nonlocal problems with measure data. https://arxiv.org/abs/2401.04549

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