A note on Sobolev-Lorentz Capacity and Hausdorff measure (2506.22042v2)

Published 27 Jun 2025 in math.AP

Abstract: 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 $n-p$.

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Authors (1)

Daniel Campbell

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