Fractional harmonic maps into manifolds in odd dimension n > 1
Fractional harmonic maps into manifolds in odd dimension n > 1
复制标题
分数调和映射到奇数维度 n > 1 的流形
DOI：
10.1007/s00526-012-0556-6
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发表时间：
2010
影响因子：
2.1
通讯作者：
F. Lio
中科院分区：
文献类型：
--
作者：
F. Lio
本文考虑了非局部能量$$\开始{array}{ll}{\mathcal{L}}_n（u）= \int_{{I\！\！R}^n}|（{-\Delta}）^{n/4} u（x）|^2 dx，\qquad（1）\end{array}$$其中是一个无边界的k维紧致光滑流形，n> 1是一个奇数。这样的临界点称为n/2-调和映射。我们证明了对每一个p ≥ 1，因此，对每一个0 < α < 1。n/2-调和映射的局部Hölder连续性是建立在[4]中关于具有反对称位势的非局部Schr dinger系统的正则性结果和一些新的3-项算子估计的基础上的。
In this paper we consider critical points of the following nonlocal energy $$\begin{array}{ll}{\mathcal{L}}_n(u) = \int_{{I\!\!R}^n}| ({-\Delta})^{n/4} u(x)|^2 dx, \qquad(1)\end{array}$$whereis a compactkdimensional smooth manifold without boundary andn> 1 is an odd integer. Such critical points are calledn/2-harmonic maps into. We prove thatfor everyp≥ 1 and thus, for every 0 < α < 1. The local Hölder continuity ofn/2-harmonic maps is based on regularity results obtained in [4] for nonlocal Schrödinger systems with an antisymmetric potential and on some new3-terms commutatorsestimates.