Search results for "Finite Perimeter"

showing 3 items of 3 documents

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
researchProduct

Rectifiability of the reduced boundary for sets of finite perimeter over RCD(K,N) spaces

2019

This paper is devoted to the study of sets of finite perimeter in RCD(K,N) metric measure spaces. Its aim is to complete the picture of the generalization of De Giorgi’s theorem within this framework. Starting from the results of Ambrosio et al. (2019) we obtain uniqueness of tangents and rectifiability for the reduced boundary of sets of finite perimeter. As an intermediate tool, of independent interest, we develop a Gauss–Green integration-by-parts formula tailored to this setting. These results are new and non-trivial even in the setting of Ricci limits. peerReviewed

Mathematics - Differential Geometryset of finite perimeterreduced boundaryrectifiabilityMetric Geometry (math.MG)RCD spacemetriset avaruudetFunctional Analysis (math.FA)Mathematics - Functional AnalysisdifferentiaaligeometriaMathematics - Metric GeometryDifferential Geometry (math.DG)Gauss–Green formulaFOS: MathematicsMathematics::Metric Geometrytangent cone
researchProduct

Sobolev and bounded variation functions on metric measure spaces

2014

International audience

[ MATH ] Mathematics [math]DifferentiabilityEquationsSets010102 general mathematicsTransport[MATH] Mathematics [math]01 natural sciencesDerivationsFine PropertiesFinite Perimeter010104 statistics & probabilityRicci Curvature BoundsLipschitz Functions0101 mathematics[MATH]Mathematics [math]InequalitiesComputingMilieux_MISCELLANEOUS
researchProduct