D. Campbell

activity

20202022

most citedApproximation of planar Sobolev

W^{2, 1}

homeomorphisms by Piecewise Quadratic Homeomorphisms and Diffeomorphisms

1 citations · 1 across the 6 of their papers we have counts for

collaborators

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5 papers · 1 filter

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…

math.AP2021

Smooth homeomorphic approximation of piecewise affine homeomorphisms

Daniel Campbell, Filip Soudský

Given any $f$ a locally finitely piecewise affine homeomorphism of $Ω\subset \rn$ onto $Δ\subset \rn$ in $W^{1, p}$ , $1 \leq p < \infty$ and any $ε > 0$ we construct a smooth injective…

math.AP2021

Classification of strict limits of planar BV homeomorphisms

Daniel Campbell, Aapo Kauranen, Emanuela Radici

We present a classification of strict limits of planar BV homeomorphisms. The authors and S. Hencl showed in a previous work \cite{CHKR} that such mappings allow for cavitations an…

math.AP2020

Diffeomorphic approximation of Planar Sobolev Homeomorphisms in rearrangement invariant spaces

Daniel Campbell, Luigi Greco, Roberta Schiattarella +1

Let $Ω \subseteq R^{2}$ be a domain, let $X$ be a rearrangement invariant space and let $f \in W^{1} X (Ω, R^{2})$ be a homeomorphism between $Ω$ and $f (Ω)$ . Then there e…

math.AP2020

A sense preserving Sobolev homeomorphism with negative Jacobian almost everywhere

Daniel Campbell, Luigi D'Onofrio, Stanislav Hencl

For every $1 \leq p < \frac{3}{2}$ we construct a Sobolev homeomorphism $f \in W^{1, p} ([- 1, 1]^{4}, [- 1, 1]^{4})$ such that $f (x) = x$ for every $x \in \partial [- 1, 1]^{4}$ but $J_{f} < 0$ a.e.