Minimizers of the Allen-Cahn energy with sub-quadratic growth
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913717751382016 |
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| author | Savin, Ovidiu Zhang, Chilin |
| author_facet | Savin, Ovidiu Zhang, Chilin |
| contents | We establish Liouville theorems for global minimizers $u$ of the Allen-Cahn energy $$\int |\nabla u|^2 + W(u) \, dx,$$ which have subquadratic growth at infinity. In particular we extend the results of \cite{S1,S3} concerning the De Giorgi's conjecture to the setting of unbounded solutions. Part of the analysis relies on the regularity of minimizers for a Dirichlet/perimeter functional which was studied by Athanasopoulous-Caffarelli-Kenig-Salsa in \cite{ACKS}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02029 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimizers of the Allen-Cahn energy with sub-quadratic growth Savin, Ovidiu Zhang, Chilin Analysis of PDEs We establish Liouville theorems for global minimizers $u$ of the Allen-Cahn energy $$\int |\nabla u|^2 + W(u) \, dx,$$ which have subquadratic growth at infinity. In particular we extend the results of \cite{S1,S3} concerning the De Giorgi's conjecture to the setting of unbounded solutions. Part of the analysis relies on the regularity of minimizers for a Dirichlet/perimeter functional which was studied by Athanasopoulous-Caffarelli-Kenig-Salsa in \cite{ACKS}. |
| title | Minimizers of the Allen-Cahn energy with sub-quadratic growth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.02029 |