On finite energy solutions of 4-harmonic and ES-4-harmonic maps (Q2050640)

The author considers 4-harmonic and ES-4-harmonic maps which are both given by a PDE of order 8. The main result of this article is that finite energy 4-harmonic and ES-4-harmonic maps \(u: \mathbb{R}^m \to N\), \(m\neq 8\) must be trivial (or harmonic if \(m=2\)). Note that the energy considered is different for 4-harmonic and ES-4-harmonic maps. In both cases the proof relies on the associated stress-energy tensor.