A compactness result for polyharmonic maps in the critical dimension
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- 作者：Shenzhou Zheng
- 关键词：polyharmonic map ; compactness ; Coulomb moving frame ; Palais ; Smale sequence ; removable singularity
- 刊名：Czechoslovak Mathematical Journal
- 出版年：2016
- 出版时间：March 2016
- 年：2016
- 卷：66
- 期：1
- 页码：137-150
- 全文大小：169 KB
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1. Department of Mathematics, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian, Beijing, 100044, China - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Analysis
Convex and Discrete Geometry
Ordinary Differential Equations
Mathematical Modeling and IndustrialMathematics - 出版者：Springer Netherlands
- ISSN：1572-9141
文摘
For n = 2m ⩽ 4, let Ω ∈ ℝ n be a bounded smooth domain and N ⊂ ℝ L a compact smooth Riemannian manifold without boundary. Suppose that {u k } ∈ W m,2(Ω, N) is a sequence of weak solutions in the critical dimension to the perturbed m-polyharmonic maps $$\frac{{\text{d}}}{{{\text{dt}}}}\left| {_{t = 0}{E_m}({\text{II}}(u + t\xi )) = 0} \right.$$ with Ω k → 0 in (W m,2(Ω, N))* and \({u_k} \rightharpoonup u\) weakly in W m,2(Ω,N). Then u is an m-polyharmonic map. In particular, the space of m-polyharmonic maps is sequentially compact for the weak-W m,2 topology. Keywords polyharmonic map compactness Coulomb moving frame Palais-Smale sequence removable singularity MSC 2010 35J35 35J48 58J05 The work was supported by the National Science Foundation of China grant 11371050.