Regularity of n/2-harmonic maps into spheres

By Armin Schikorra. 2010

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We prove Holder continuity for n/2-harmonic maps from arbitrary 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 Wenteʼs 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. This work was the authorʼs PhD thesis, written in March 2010.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cd2f24c59f3f60957bf96921c8f72f4eb662544d

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Nonlinear commutators for the fractional p-Laplacian and applications (2015, unknown): “[8, 7, 5, 3, 21, 19, 20], and we will not repeat them in detail.”
On a new class of fractional partial differential equations (2014, background): “A more technical Sobolev inequality involving the Lorentz spaces can also be deduced for the fractional gradient, see the work [27, 29] for these estimates in the context of the fractional Laplacian.”