D. Campbell

activity

20202025

most citedApproximation of planar Sobolev

W^{2, 1}

homeomorphisms by Piecewise Quadratic Homeomorphisms and Diffeomorphisms

1 citations · 2 across the 12 of their papers we have counts for

collaborators

13 papers

math.AP2025

Diffeomorphic approximation of piecewise affine homeomorphisms

Daniel Campbell, Luigi D'Onofrio, Tomáš Vítek

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

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.AP2024

Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity

Daniel Campbell

We present three novel classifications of the weak sequential (and strong) limits in $W^{1, p}$ of planar diffeomorphisms. We introduce a concept called the QM condition which is a…

math.AP2022★ 1 cited

Classification of area-strict limits of planar BV homeomorphisms

Daniel Campbell, Aapo Kauranen, Emanuela Radici

We present a classification of area-strict limits of planar $B V$ homeomorphisms. This class of mappings allows for cavitations and fractures but fulfil a suitable generalization of…

math.AP2022

Minimal Extension for the $α$ -Manhattan norm

Daniel Campbell, Aapo Kauranen, Emanuela Radici

Let $\partial Q$ be the boundary of a convex polygon in $R^{2}$ , $e_{α} = (cos α, sin α)$ and $e_{α}^{⊥} = (- sin α, cos α)$ be a basis of $R^{2}$ for some $…

math.AP2022

Injectivity in second-gradient Nonlinear Elasticity

D. Campbell, S. Hencl, A. Menovschikov +1

We study injectivity for models of Nonlinear Elasticity that involve the second gradient. We assume that $Ω \subset R^{n}$ is a domain, $f \in W^{2, q} (Ω, R^{n})$ satisfie…