Fine properties of functions with bounded variation in Carnot-Carathéodory spaces
Don, S., & Vittone, D. (2019). Fine properties of functions with bounded variation in Carnot-Carathéodory spaces. Journal of Mathematical Analysis and Applications, 479(1), 482-530. https://doi.org/10.1016/j.jmaa.2019.06.035
Published inJournal of Mathematical Analysis and Applications
© 2019 Elsevier Inc.
We study properties of functions with bounded variation in Carnot-Carathéodory spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives. Under an additional assumption on the space, called property R, we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative.
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Related funder(s)Academy of Finland; European Commission
Funding program(s)Academy Research Fellow, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingThe authors are supported by the University of Padova Project Networking and STARS Project “Sub-Riemannian Geometry and Geometric Measure Theory Issues: Old and New” (SUGGESTION), and by GNAMPA of INdAM (Italy) project “Campi vettoriali, superfici e perimetri in geometrie singolari”. The second named author wishes to acknowledge the support and hospitality of FBK-CIRM (Trento), where part of this paper was written. The first named author has been partially supported by the Academy of Finland (grant 288501 “Geometry of subRiemannian groups”) and by the European Research Council (ERC Starting Grant 713998 GeoMeG “Geometry of Metric Groups”). ...
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