Calculus of Variations and Geometric Measure Theory
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A. Carbotti - S. Don - D. Pallara - A. Pinamonti

Local minimizers and Gamma-convergence for nonlocal perimeters in Carnot Groups

created by carbotti on 05 Apr 2020
modified on 01 Jun 2020

[BibTeX]

Submitted Paper

Inserted: 5 apr 2020
Last Updated: 1 jun 2020

Pages: 30
Year: 2020

ArXiv: 2004.02314 PDF

Abstract:

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.

Tags: GeoMeG
Keywords: Carnot groups, Sets of finite perimeter, Rectifiability, $\Gamma$-convergence, calibrations, nonlocal perimeters


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