2010/03/31 by Armin Schikorra · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #msc:35B65 #msc:35J60 #msc:35S05 #msc:58E20
paper · pdf · doi:10.1016/j.jde.2011.08.021
some details added, some errors removed. new introduction
arxiv created 2010/06/28 · openalex publication_date 2011/09/07 · arxiv updated 2013/01/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02
We prove Hoelder 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.