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RESEARCH PRODUCT

Fine properties of functions with bounded variation in Carnot-Carathéodory spaces

Davide VittoneSebastiano Don

subject

Pure mathematicsApplied Mathematics010102 general mathematicsvariaatiolaskentaCarnot-Carathéodory spaces; Functions with bounded variationType (model theory)Classification of discontinuitiesSpace (mathematics)01 natural sciencesdifferentiaaligeometria010101 applied mathematicsDiscontinuity (linguistics)Functions with bounded variationBounded variationCarnot-Carathéodory spacesJumpAlmost everywheremittateoriaDifferentiable function0101 mathematicsfunctions with bounded variationfunktiotAnalysisMathematics

description

Abstract We study properties of functions with bounded variation in Carnot-Caratheodory 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.

yearjournalcountryeditionlanguage
2019-11-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2019.06.035