A nonlocal approximation of the Gaussian perimeter: Gamma convergence and Isoperimetric properties
Analysis of PDEs
2020-11-17 v1
Abstract
We study a non local approximation of the Gaussian perimeter, proving the Gamma convergence to the local one. Surprisingly, in contrast with the local setting, the halfspace turns out to be a volume constrained stationary point if and only if the boundary hyperplane passes through the origin. In particular, this implies that Ehrhard symmetrization can in general increase the considered non local Gaussian perimeter.
Keywords
Cite
@article{arxiv.2011.07544,
title = {A nonlocal approximation of the Gaussian perimeter: Gamma convergence and Isoperimetric properties},
author = {Antonio De Rosa and Domenico Angelo La Manna},
journal= {arXiv preprint arXiv:2011.07544},
year = {2020}
}