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arXiv · 2608.28336

H\"older regularity for nonlocal equations governed by measures and non-standard growth

Luke Schleef
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Abstract

On doubling metric measure spaces, we study nonlocal operators with non-standard $(p,q)$-Orlicz growth ($1<p\leq q<\infty$), where the interaction kernel is given by a general, non-translation-invariant measure. Under natural assumptions on the interaction measure - namely symmetry, a suitable nonlocal Poincar\'{e} inequality, and a tail bound - we prove that every weak solution to the corresponding homogeneous nonlocal equation admits a locally H\"older continuous representative. These regularity results are new even in the Euclidean setting.

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Luke Schleef. 2026-08-28. H\"older regularity for nonlocal equations governed by measures and non-standard growth. https://arxiv.org/abs/2608.28336

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