Local minimizers in $3$d of vector Allen-Cahn with a quadruple junction
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908669158883328 |
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| author | Adimurthi, Abhishek Sternberg, Peter |
| author_facet | Adimurthi, Abhishek Sternberg, Peter |
| contents | For $Ω$ a perturbation of the unit ball in $\mathbb{R}^3$, we establish the existence of a sequence of local minimizers for the vector Allen-Cahn energy. The sequence converges in $L^1$ to a partition of $Ω$ whose skeleton is given by a tetrahedral cone and thus contains a quadruple point. This is accomplished by proving that the partition is an isolated local minimizer of a weighted perimeter problem arising as the associated $Γ$-limit of the sequence of Allen-Cahn functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17687 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local minimizers in $3$d of vector Allen-Cahn with a quadruple junction Adimurthi, Abhishek Sternberg, Peter Analysis of PDEs Optimization and Control 49, 35 For $Ω$ a perturbation of the unit ball in $\mathbb{R}^3$, we establish the existence of a sequence of local minimizers for the vector Allen-Cahn energy. The sequence converges in $L^1$ to a partition of $Ω$ whose skeleton is given by a tetrahedral cone and thus contains a quadruple point. This is accomplished by proving that the partition is an isolated local minimizer of a weighted perimeter problem arising as the associated $Γ$-limit of the sequence of Allen-Cahn functionals. |
| title | Local minimizers in $3$d of vector Allen-Cahn with a quadruple junction |
| topic | Analysis of PDEs Optimization and Control 49, 35 |
| url | https://arxiv.org/abs/2502.17687 |