Second order expansion for the nonlocal perimeter functional
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 en...
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| Main Authors: | , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
24 Oct 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-30 |
| DOI: | 10.48550/arXiv.2110.12378 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.48550/arXiv.2110.12378 Verlag, kostenfrei, Volltext: http://arxiv.org/abs/2110.12378 
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| Author Notes: | Hans Knüpfer and Wenhui Shi |
| Summary: | 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. |
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| Item Description: | Gesehen am 09.01.2024 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2110.12378 |