Calculus of Variations and Geometric Measure Theory

A. De Rosa - D. A. La Manna

A nonlocal approximation of the Gaussian perimeter: Gamma convergence and Isoperimetric properties

created by derosa on 20 Nov 2020
modified on 11 Jan 2022


Published Paper

Inserted: 20 nov 2020
Last Updated: 11 jan 2022

Journal: Comm. Pure Appl. Anal.
Year: 2021

ArXiv: 2011.07544 PDF


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.