D. Campbell

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math.AP2025

A note on Sobolev-Lorentz Capacity and Hausdorff measure

Daniel Campbell

In this paper we give an elementary proof that sets of zero $p, 1$ -Sobolev-Lorentz capacity are $H^{n - p}$ -null sets independently of non-linear potential theory. We furthe…

math.AP2025

Diffeomorphic approximation of piecewise affine homeomorphisms

Daniel Campbell, Luigi D'Onofrio, TomÃ¡Å¡ VÃtek

Given any $f$ a locally finitely piecewise affine homeomorphism of $I^c ◯ \subset R^{d}$ onto $I^ \subset R^{d}$ (for $d = 3, 4$ ) such that $f \in W^{1, p} (I^c ◯, R^{d})$ …