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.
Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups
Alessandro Carbotti;Diego Pallara;
2021-01-01
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.File in questo prodotto:
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