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A compactness theorem of \(n\)-harmonic maps. (English) Zbl 1229.58017
Summary: For \(n\geq 3\), let \(\Omega\subset \mathbb R^n\) be a bounded domain and \(N\subset\mathbb R^L\) be a compact smooth Riemannian submanifold without boundary. Suppose that \(\{u_n\}\subset W^{1,n}(\Omega,N)\) are weak solutions to a (perturbed) \(n\)-harmonic map equation satisfying a limit condition, and \(u_k\to u\) weakly in \(W^{1,n}(\Omega,N)\). Then \(u\) is an \(n\)-harmonic map. In particular, the space of \(n\)-harmonic maps is sequentially compact for the weak-\(W^{1,n}\) topology.

MSC:
58E20 Harmonic maps, etc.
35J60 Nonlinear elliptic equations
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