Regularity of n/2-harmonic maps into spheres
Regularity of n/2-harmonic maps into spheres
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DOI：
10.1016/j.jde.2011.08.021
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发表时间：
2010-03
影响因子：
2.4
通讯作者：
A. Schikorra
中科院分区：
文献类型：
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作者：
A. Schikorra
证明了从Rn的任意子集到球面的n/2-调和映射的Hölder连续性。这将F.Da Lio和T.Rivière最近的一维结果推广到任意维度。证明依赖于补偿效应，我们采用L.Tartar对WenteʼS不等式的一种方法来量化补偿效应，而不是一维情形中使用的Besov空间论点。此外，还发展和应用了Hodge分解和高阶Poincaré不等式的分数阶类似，以及与分数阶拉普拉斯算子类似的非局部算子的几种局部化效应。本文是作者ʼS的博士论文，撰写于2010年3月。
We prove Hölder continuity for n/2-harmonic maps from arbitrary subsets of Rninto a sphere. This extends a recent one-dimensional result by F. Da Lio and T. Rivière 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 Poincaré 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.