3 citations · 5 across the 11 of their papers we have counts for
11 papers
Magnitude and diversity of trees
Philippe Bouafia
We compute the magnitude (an isometric invariant of metric spaces) of compact -trees and show that it equals , where denotes the total leng…
Another simple proof of the 1-dimensional flat chain conjecture
Philippe Bouafia, Thierry De Pauw
We provide a short proof of the 1-dimensional flat chain conjecture.
Non-absolute integration and application to Young geometric integration
Philippe Bouafia
We survey several non-absolutely convergent integrals, including the Henstock-Kurzweil and Pfeffer integrals, and use ideas from these theories to investigate the problem of multid…
Fractional currents and Young geometric integration
Philippe Bouafia
We introduce a class of flat currents with fractal properties, called fractional currents, which satisfy a compactness theorem and remain stable under pushforwards by Hölder contin…
On the exterior product of Hölder differential forms
Philippe Bouafia
We introduce a complex of cochains, -fractional charges (), whose regularity is between that of De Pauw-Moonens-Pfeffer's charges and that of Whitney's flat cochain…
A regularity property of fractional Brownian sheets
Philippe Bouafia, Thierry De Pauw
A function defined on is called strongly chargeable if there is a continuous vector-field such that equals the flux of through the rectan…
Young Integration with respect to Hölder Charges
Philippe Bouafia
We present a multidimensional Young integral that enables to integrate Hölder continuous functions with respect to a Hölder charge. It encompasses the integration of Hölder differe…
A representation formula for members of SBV dual
Philippe Bouafia, Thierry De Pauw
We give an integral representation formula for members of the dual of in terms of functions that are defined on , an appropriate fiber space…
Localizable locally determined measurable spaces with negligibles
Philippe Bouafia, Thierry De Pauw
We study measurable spaces equipped with a -ideal of negligible sets. We find conditions under which they admit a localizable locally determined version -- a kind of fiber space…
Existence of harmonic multiple valued maps into a separable Hilbert space
Philippe Bouafia, Thierry De Pauw, Jordan Goblet
The general existence of -Dirichlet energy minimizing maps into is obtained.
Multiple valued maps into a separable Hilbert space that almost minimize their Dirichlet energy or are squeeze and squash stationary
Philippe Bouafia, Thierry De Pauw, Changyou Wang
Let $f : U\subset\Rm \to \calQ_Q(\ell_2)$ be of Sobolev class , . If almost minimizes its Dirichlet energy then is Hölder continuous. If …