Uniqueness of the blow-down limit for triple junction problem
| Autor: | Geng, Zhiyuan |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 29 pages |
| Databáze: | arXiv |
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