D. Campbell

most citedApproximation of planar Sobolev

W^{2, 1}

homeomorphisms by Piecewise Quadratic Homeomorphisms and Diffeomorphisms

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

collaborators

3 papers

math.FA2020★ 1 cited

Approximation of planar Sobolev $W^{2, 1}$ homeomorphisms by Piecewise Quadratic Homeomorphisms and Diffeomorphisms

Daniel Campbell, Stanislav Hencl

Given a Sobolev homeomorphism $f \in W^{2, 1}$ in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of $ε$ measure. We show that this piecewise q…

math.FA2020

Comparison between the non-crossing and the non-crossing on lines properties

Daniel Campbell, Aldo Pratelli, Emanuela Radici

In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions…

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.

Approximation of planar Sobolev W2,1 homeomorphisms by Piecewise Quadratic Homeomorphisms and Diffeomorphisms

Comparison between the non-crossing and the non-crossing on lines properties

A sense preserving Sobolev homeomorphism with negative Jacobian almost everywhere

Approximation of planar Sobolev $W^{2, 1}$ homeomorphisms by Piecewise Quadratic Homeomorphisms and Diffeomorphisms