0000000000237684

AUTHOR

Diego Pallara

0000-0002-1909-484x

showing 2 related works from this author

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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Gamma-convergence of Gaussian fractional perimeter

2021

Abstract We prove the Γ-convergence of the renormalised Gaussian fractional s-perimeter to the Gaussian perimeter as s → 1 - {s\to 1^{-}} . Our definition of fractional perimeter comes from that of the fractional powers of Ornstein–Uhlenbeck operator given via Bochner subordination formula. As a typical feature of the Gaussian setting, the constant appearing in front of the Γ-limit does not depend on the dimension.

Gamma-convergenceApplied MathematicsOperator (physics)GaussianMathematical analysisPerimetersymbols.namesakeDimension (vector space)Fractional perimeters Gamma-convergence Gaussian analysisConvergence (routing)Fractional perimetersymbolsConstant (mathematics)AnalysisMathematicsGaussian analysis
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