Regularity and uniqueness of the heat flow of biharmonic maps
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arXiv
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| Format: | Preprint |
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2012
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| _version_ | 1866915361711980544 |
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| author | Hineman, Jay Huang, Tao Wang, Changyou |
| author_facet | Hineman, Jay Huang, Tao Wang, Changyou |
| contents | 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). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1208_4287 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Regularity and uniqueness of the heat flow of biharmonic maps Hineman, Jay Huang, Tao Wang, Changyou Analysis of PDEs 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). |
| title | Regularity and uniqueness of the heat flow of biharmonic maps |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1208.4287 |