Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups
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 Γ-liminf of the rescaled energy in terms of the horizontal perimeter.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
EDP Sciences
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202109014750Use this for linking
Review status
Peer reviewed
ISSN
1292-8119
DOI
https://doi.org/10.1051/cocv/2020055
Language
English
Published in
ESAIM : Control, Optimisation and Calculus of Variations
Citation
- Carbotti, A., Don, S., Pallara, D., & Pinamonti, A. (2021). Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups. ESAIM : Control, Optimisation and Calculus of Variations, 27(Supplement), Article S11. https://doi.org/10.1051/cocv/2020055
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Funder(s)
Research Council of Finland
European Commission
Research Council of Finland
Funding program(s)
Academy Research Fellow, AoF
ERC Starting Grant
Academy Project, AoF
Akatemiatutkija, SA
ERC Starting Grant
Akatemiahanke, SA
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Additional information about funding
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).
Copyright© EDP Sciences, SMAI 2021