A note on Sobolev-Lorentz Capacity and Hausdorff measure

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Bibliographic Details
Main Author:	Campbell, Daniel
Format:	Preprint
Published:	2025
Subjects:	Analysis of PDEs
Online Access:	Acceder al recurso
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author	Campbell, Daniel
author_facet	Campbell, Daniel
contents	In this paper we give an elementary proof that sets of zero $p,1$-Sobolev-Lorentz capacity are $\mathcal{H}^{n-p}$-null sets independently of non-linear potential theory. We further show that there exists a set of Sobolev-Lorentz-$(p,1)$ capacity equal zero with Hausdorff dimension equal $n-p$.
format	Preprint
id	arxiv_https___arxiv_org_abs_2506_22042
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	A note on Sobolev-Lorentz Capacity and Hausdorff measure Campbell, Daniel Analysis of PDEs In this paper we give an elementary proof that sets of zero $p,1$-Sobolev-Lorentz capacity are $\mathcal{H}^{n-p}$-null sets independently of non-linear potential theory. We further show that there exists a set of Sobolev-Lorentz-$(p,1)$ capacity equal zero with Hausdorff dimension equal $n-p$.
title	A note on Sobolev-Lorentz Capacity and Hausdorff measure
topic	Analysis of PDEs
url	https://arxiv.org/abs/2506.22042

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