A boundary monotonicity inequality for variationally biharmonic maps and applications to regularity theory
- 29 Downloads
We derive a boundary monotonicity formula for a class of biharmonic maps with Dirichlet boundary conditions. A monotonicity formula is crucial in the theory of partial regularity in supercritical dimensions. As a consequence of such a boundary monotonicity formula, one is able to show partial regularity for variationally biharmonic maps and full boundary regularity for minimizing biharmonic maps.
KeywordsBiharmonic maps Boundary monotonicity inequality Regularity
I would like to thank Prof. Dr. Christoph Scheven for his much helpful advice.
- 1.Altuntas, S.: Derivation of a boundary monotonicity inequality for variationally biharmonic maps (download under https://arxiv.org/pdf/1711.03348.pdf) (2017)
- 10.Mazowiecka, K.E.: Singularities of harmonic and biharmonic maps into compact manifolds, PhD Dissertation (2017)Google Scholar
- 12.Moser, R.: A variational problem pertaining to biharmonic maps. Commun. Partial Differ. Equ. 33(9), 1654–1689 (2008). https://doi.org/10.1080/03605300802224698
- 19.Simon, L.: Theorems on regularity and singularity of energy minimizing maps. ETH Lecture Notes, Birkhäuser, Zürich (1996)Google Scholar