Second order expansion for the nonlocal perimeter functional

• Verfasst von: Knüpfer, Hans [VerfasserIn]
• Verfasst von: Shi, Wenhui [VerfasserIn]
• Titel: Second order expansion for the nonlocal perimeter functional
• Verf.angabe: Hans Knüpfer and Wenhui Shi
• E-Jahr: 2021
• Jahr: 24 Oct 2021
• Umfang: 30 S.
• Fussnoten: Gesehen am 09.01.2024
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [Erscheinungsort nicht ermittelbar] : Arxiv.org, 1991
• Jahr Quelle: 2021
• Band/Heft Quelle: (2021), Artikel-ID 2110.12378, Seite 1-30
• DOI: doi:10.48550/arXiv.2110.12378
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Mathematics - Analysis of PDEs
• K10plus-PPN: 1816986682

Abstract

The seminal results of Bourgain, Brezis, Mironescu and Dávila show that the classical perimeter can be approximated by a family of nonlocal perimeter functionals. We consider a corresponding second order expansion for the nonlocal perimeter functional. In a special case, the considered family of energies is also relevant for a variational model for thin ferromagnetic films. We derive the Gamma--limit of these functionals. We also show existence for minimizers with prescribed volume fraction. For small volume fraction, the unique, up to translation, minimizer of the limit energy is given by the ball. The analysis is based on a systematic exploitation of the associated symmetrized autocorrelation function.