6533b7d4fe1ef96bd1262aef

RESEARCH PRODUCT

Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups

Alessandro CarbottiSebastiano DonAndrea PinamontiDiego Pallara

subject

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)

description

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.

yearjournalcountryeditionlanguage
2020-04-05ESAIM: Control, Optimisation and Calculus of Variations
https://doi.org/10.1051/cocv/2020055