Regularity of n/2-harmonic maps into spheres
- Regularität von n/2-harmonischen Abbildungen in Sphären
Schikorra, Armin; von der Mosel, Heiko (Thesis advisor)
Aachen : Publikationsserver der RWTH Aachen University (2010)
Dissertation / PhD Thesis
Aachen, Techn. Hochsch., Diss., 2010
We prove Hölder continuity for n/2-harmonic maps from subsets of Rn into a sphere. This extends a recent one-dimensional result by F. Da Lio and T. Riviere to arbitrary dimensions. The proof relies on compensation effects which we quantify adapting an approach for Wente's inequality by L. Tartar, instead of Besov-space arguments which were used in the one-dimensional case. Moreover, fractional analogues of Hodge decomposition and higher order Poincare inequalities as well as several localization effects for nonlocal operators similar to the fractional laplacian are developed and applied.