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Functions of bounded fractional variation and fractal currents
Prof. Roger Zuest
1:00-2:00pm, Friday June 21st, 2019  ãÉÐÐÊýÑ§Â¥102±¨¸æÌü

Time£º1:00-2:00pm, Friday June 21st, 2019
¡¡¡¡¡¡1:00-3:00pm, Monday June 24th, 2019

Abstract:
Extending the space of functions with bounded variation $BV(\mathbb R^n)$ we propose a notion of functions with fractional bounded variation $BV^\alpha(\mathbb R^n)$ for some $\alpha \in [0,1]$. The goal is to motivate this definition and give some properties thereof. As we will see, an interesting class that fits into this setting are characteristic functions of domains with fractal boundaries. Further we characterize functions of bounded fractional variation as a certain subspace of flat chains in the sense of Whitney and as multilinear functionals in the setting of currents in metric spaces as introduced by Ambrosio and Kirchheim. Consequently we discuss extensions to H?lder differential forms, higher integrability, an isoperimetric inequality and a Lusin type property.

Host£ºProf. Thierry De Pauw