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Local minimizers and Gamma-convergence for nonlocal perimeters in Carnot Groups (2004.02314v1)
Published 5 Apr 2020 in math.AP and math.MG
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.
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