A1 Journal article (refereed)
A non local approximation of the Gaussian perimeter : Gamma convergence and Isoperimetric properties (2021)

De Rosa, A., & La Manna, D. A. (2021). A non local approximation of the Gaussian perimeter : Gamma convergence and Isoperimetric properties. Communications on Pure and Applied Analysis, 20(5), 2101-2116. https://doi.org/10.3934/cpaa.2021059

JYU authors or editors

Publication details

All authors or editors: De Rosa, Antonio; La Manna, Domenico Angelo

Journal or series: Communications on Pure and Applied Analysis

ISSN: 1553-5258

eISSN: 1553-5258

Publication year: 2021

Volume: 20

Issue number: 5

Pages range: 2101-2116

Publisher: American Institute of Mathematical Sciences (AIMS)

Publication country: United States

Publication language: English

DOI: https://doi.org/10.3934/cpaa.2021059

Publication open access: Not open

Publication channel open access: 

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2011.07544

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 non local Gaussian perimeter taken into consideration.

Keywords: measure theory; calculus of variations; integral equations; approximation

Free keywords: gamma convergence; Gauss space; non local perimeter; isoperimetric problem; Ehrhard symmetrization

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Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 1