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- Title
On Finite Energy Solutions of 4-harmonic and ES-4-harmonic Maps.
- Authors
Branding, Volker
- Abstract
4-harmonic and ES-4-harmonic maps are two generalizations of the well-studied harmonic map equation which are both given by a nonlinear elliptic partial differential equation of order eight. Due to the large number of derivatives it is very difficult to find any difference in the qualitative behavior of these two variational problems. In this article we prove that finite energy solutions of both 4-harmonic and ES-4-harmonic maps from Euclidean space must be trivial. However, the energy that we require to be finite is different for 4-harmonic and ES-4-harmonic maps pointing out a first difference between these two variational problems.
- Publication
Journal of Geometric Analysis, 2021, Vol 31, Issue 8, p8666
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-021-00610-7