تقرير
Regularity and uniqueness of the heat ow of biharmonic maps
| العنوان: | Regularity and uniqueness of the heat ow of biharmonic maps |
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| المؤلفون: | Hineman, Jay, Huang, Tao, Wang, Changyou |
| سنة النشر: | 2012 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs |
| الوصف: | In this paper, we first establish regularity of the heat flow of biharmonic maps into the unit sphere $S^L\subset\mathbb R^{L+1}$ under a smallness condition of renormalized total energy. For the class of such solutions to the heat flow of biharmonic maps, we prove the properties of uniqueness, convexity of hessian energy, and unique limit at time infinity. We establish both regularity and uniqueness for the class of weak solutions $u$ to the heat flow of biharmonic maps into any compact Riemannian manifold $N$ without boundary such that $\nabla^2 u\in L^q_tL^p_x$ for some $p>n/2$ and $q>2$ satisfying (1.13). Comment: Two errors in the proof of proposition 2.2 have been fixed, as a consequence the range of the power $p$ through the main theorems of the paper is required to $p>3/2$ |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1208.4287 |
| رقم الأكسشن: | edsarx.1208.4287 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |