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A compactness theorem of $n$-harmonic maps | Changyou Wang
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4 May 2004 | Subject: | Analysis of PDEs; Differential Geometry MSC-class: 58E20 | math.AP math.DG | Abstract: | For $nge 3$, let $Omega$ be a bounded domain in $R^n$ and $N$ be a compact Riemannian manifold in $R^L$ without boundary. Suppose that $u_nin W^{1,n}(Omega,N)$ are the Palais-Smale sequences of the Dirichlet $n$-energy functional and $u_n$ converges weakly in $W^{1,n}$ to a map $uin W^{1,n}(Omega,N)$. Then $u$ is a $n$-harmonic map. In particular, the space of $n$-harmonic maps is sequentially compact for the weak $W^{1,n}$-topology. | Source: | arXiv, math.AP/0405058 | Services: | Forum | Review | PDF | Favorites |
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