Remarks on biharmonic maps into spheres

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Biharmonic maps from R4 into a Riemannian manifold (2004, methodology): “To overcome this difficulty, we first utilize the smallness of �∇ u� L4(B1) to get a family of smooth maps {u� }⊂ C ∞ (B1 ,N ), approximating u strongly in W 1 ,4 , such that �∇ u� � L4(B1) is small, uniformly with respect to �> 0. It follows from the triviality of (u� ) ∗ TN on B1 that we can find”
Conservation Laws for Fourth Order Systems in Four Dimensions (2006, methodology): “The regularity of solutions of special cases of (1.12) was first studied by Wang (2004a).”
On biharmonic maps and their generalizations (2003, unknown): “Wang obtained, in a series of recent preprints [ 35 ], [36] and [37], another new proof of Theorem 1.1 and of Proposition 2.1.”
A short survey on biharmonic maps between Riemannian manifolds (2005, background): “We shall not report on this aspect and we refer the reader to [33, 34, 53, 54, 55] and the references therein.”