On removable singularities of certain harmonic maps
A weakly harmonic map \(u\in H^ 1(\Omega,M)\cap L^{\infty}(\Omega,M)\) of a domain \(\Omega \subset {\mathbb{R}}^ n\) into a Riemannian manifold \(M(\subset {\mathbb{R}}^ k)\) is said to be stationary if the energy of u precomposed with any 1-parameter family of diffeomorphisms (with compact support in \(\Omega)\) is stable up to first order. The main result here is a removable singularity theorem which states that, for \(\Omega =ball\), any stationary map u which is \(C^ 2\) in \(B\setminus\) center extends smoothly to B provided that \(\int_{B}| Du|^ n dx<\infty\).
scientific article; zbMATH DE number 3977977