Uniqueness of the blow-down limit for triple junction problem
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914739937869824 |
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| author | Geng, Zhiyuan |
| author_facet | Geng, Zhiyuan |
| contents | We prove the uniqueness of $L^1$ blow-down limit at infinity for an entire minimizing solution $u:\mathbb{R}^2\rightarrow\mathbb{R}^2$ of a planar Allen-Cahn system with a triple-well potential. Consequently, $u$ can be approximated by a triple junction map at infinity. The proof exploits a careful analysis of energy upper and lower bounds, ensuring that the diffuse interface remains within a small neighborhood of the approximated triple junction at all scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniqueness of the blow-down limit for triple junction problem Geng, Zhiyuan Analysis of PDEs 35J47, 35J50, 35B08, 35A02 We prove the uniqueness of $L^1$ blow-down limit at infinity for an entire minimizing solution $u:\mathbb{R}^2\rightarrow\mathbb{R}^2$ of a planar Allen-Cahn system with a triple-well potential. Consequently, $u$ can be approximated by a triple junction map at infinity. The proof exploits a careful analysis of energy upper and lower bounds, ensuring that the diffuse interface remains within a small neighborhood of the approximated triple junction at all scales. |
| title | Uniqueness of the blow-down limit for triple junction problem |
| topic | Analysis of PDEs 35J47, 35J50, 35B08, 35A02 |
| url | https://arxiv.org/abs/2404.02859 |