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arXiv · 2506.05037

Limits at infinity for Haj{\l}asz-Sobolev functions in metric spaces

Angha Agarwal·Antti V. Vähäkangas
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Abstract

We study limits at infinity for homogeneous Hajlasz-Sobolev functions defined on uniformly perfect metric spaces equipped with a doubling measure. We prove that a quasicontinuous representative of such a function has a pointwise limit at infinity outside an exceptional set, defined in terms of a variational relative capacity. Our framework refines earlier approaches that relied on Hausdorff content rather than relative capacity, and it extends previous results for homogeneous Newtonian and fractional Sobolev functions.

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Angha Agarwal, Antti V. Vähäkangas. 2025-06-05. Limits at infinity for Haj{\l}asz-Sobolev functions in metric spaces. https://arxiv.org/abs/2506.05037

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