Volume 27, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Number of page(s)||27|
|Published online||01 March 2021|
Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups*
Dipartimento di Matematica e Fisica, Università del Salento, Via Per Arnesano,
2 Department of Mathematics and Statistics, P.O. Box 35 (MaD), 40014, University of Jyväskylä, Finland.
3 Dipartimento di Matematica e Fisica, Università del Salento, and INFN, Sezione di Lecce, Via Per Arnesano, 73100 Lecce, Italy.
4 Dipartimento di Matematica, Università di Trento, Via Sommarive, 14, 38123 Povo, TN, Italy.
** Corresponding author: firstname.lastname@example.org
Accepted: 8 August 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 Γ-liminf of the rescaled energy in terms of the horizontal perimeter.
Mathematics Subject Classification: 53C17 / 22E25 / 49Q15 / 53C38 / 26A33 / 49Q05
Key words: Carnot groups / calibrations / nonlocal perimeters / Γ-convergence / sets of finite perimeter / rectifiability
S.D. has been partially supported by the Academy of Finland (grant 288501 “Geometry of subRiemannian groups” and grant 322898 “Sub-Riemannian geometry via metric-geometry and Lie-group theory”) and by the European Research Council (ERC Starting Grant 713998 GeoMeG “Geometry of metric groups”). D.P. is member of G.N.A.M.P.A. of the Italian Istituto Nazionale di Alta Matematica (INdAM) and has been partially supported by the PRIN 2015 MIUR project 2015233N54. A.P. is member of G.N.A.M.P.A. of the Italian Istituto Nazionale di Alta Matematica (INdAM).
© EDP Sciences, SMAI 2021
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