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Czechoslovak Mathematical Journal

, Volume 66, Issue 1, pp 137–150 | Cite as

A compactness result for polyharmonic maps in the critical dimension

  • Shenzhou ZhengEmail author
Article
  • 60 Downloads

Abstract

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 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Jiaotong UniversityHaidian, BeijingChina

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