Partial regularity for biharmonic maps, revisited
Using gauge theory, the author gives a new proof for the partial regularity of stationary (extrinsically) biharmonic maps of domains in \(\mathbb R^m\), \(m>4\). The paper continues studies from [\textit{T. Rivière} and \textit{M. Struwe}, Commun. Pure Appl. Math. 61, 451--463 (2008; Zbl 1144.58011)] where harmonic maps are discussed. The critical \(m=4\) case has been considered in [\textit{T. Lamm} and \textit{T. Rivière}, Commun. Partial Differ. Equations 33, 245--262 (2008; Zbl 1139.35328)]. The proof is based on writing the nonlinearity in a way that allows the use of the Coulomb gauge theorems by Meyer and Rivière, Tao and Tian. Actually, this gives a new proof for the partial regularity that has been proven in [\textit{C. Wang}, Commun. Pure Appl. Math. 57, 419--444 (2004; Zbl 1055.58008)]. In an appendix, some details are given which may help clarify the previous proof.
scientific article; zbMATH DE number 5304002