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arXiv · 2307.01743

Regularity theory for nonlocal equations with general growth in the Heisenberg group

Yuzhou Fang·Chao Zhang
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Abstract

We deal with a wide class of generalized nonlocal $p$-Laplace equations, so-called nonlocal $G$-Laplace equations, in the Heisenberg framework. Under natural hypotheses on the $N$-function $G$, we provide a unified approach to investigate in the spirit of De Giorgi-Nash-Moser theory, some local properties of weak solutions to such kind of problems, involving boundedness, H\"{o}lder continuity and Harnack inequality. To this end, an improved nonlocal Caccioppoli-type estimate as the main auxiliary ingredient is exploited several times.

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Yuzhou Fang, Chao Zhang. 2023-07-04. Regularity theory for nonlocal equations with general growth in the Heisenberg group. https://arxiv.org/abs/2307.01743

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