تقرير
Uniqueness of the blow-down limit for triple junction problem
| العنوان: | Uniqueness of the blow-down limit for triple junction problem |
|---|---|
| المؤلفون: | Geng, Zhiyuan |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35J47, 35J50, 35B08, 35A02 |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.02859 |
| رقم الأكسشن: | edsarx.2404.02859 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |