0000000000215092

AUTHOR

Sebastiano Don

0000-0002-7881-742x

showing 2 related works from this author

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

2019

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.

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 variationfunktiotAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups

2020

We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in which the De Giorgi's rectifiability Theorem holds, we provide a lower bound for the $\Gamma$-liminf of the rescaled energy in terms of the horizontal perimeter.

Class (set theory)Pure mathematicsControl and OptimizationCarnot groups calibrations nonlocal perimeters/ Γ-convergence sets of finite perimeter rectifiabilityMathematics::Analysis of PDEssets of finite perimetervariaatiolaskentaComputer Science::Computational Geometry01 natural sciencesUpper and lower boundsdifferentiaaligeometriasymbols.namesakeMathematics - Analysis of PDEs510 MathematicsMathematics - Metric GeometryComputer Science::Logic in Computer ScienceConvergence (routing)FOS: MathematicsMathematics::Metric Geometry0101 mathematicscalibrationsMathematicsnonlocal perimeters010102 general mathematicsrectifiabilityryhmäteoriaMetric Geometry (math.MG)matemaattinen optimointi010101 applied mathematicsComputational MathematicsΓ-convergenceΓ-convergenceCarnot groupsControl and Systems EngineeringsymbolsCarnot cycleAnalysis of PDEs (math.AP)ESAIM: Control, Optimisation and Calculus of Variations
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