Integro-Differential Harmonic Maps into Spheres
Integro-Differential Harmonic Maps into Spheres
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DOI：
10.1080/03605302.2014.974059
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发表时间：
2014-01
影响因子：
1.9
通讯作者：
A. Schikorra
中科院分区：
文献类型：
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作者：
A. Schikorra
对于S∈(0，1)，我们引入了(积分-微分)调和映射v：Ω⊂ℝn→ℝN，定义为Gagliardo/Slobodeckij能量的临界点，条件是v(Ω)⊂𝕊N−1，对于(N−1)球面𝕊N−1⊂ℝN.当p=2时，这是Da Lio和Rivière最先考虑的经典分数次调和映射。对于p≠2，这是一种具有简并的非定域欧拉-拉格朗日方程的新能量。它们不同于Lio和作者介绍的n/p-调和映射，必须用新的论点来处理，这可能对几何能量的进一步应用具有独立的意义。主要结果是这些映射在临界情况下的Hölder连续性。
For s ∈ (0, 1) we introduce (integro-differential) harmonic maps v: Ω ⊂ ℝ n → ℝ N , which are defined as critical points of the Gagliardo/Slobodeckij energy with the condition that v(Ω) ⊂ 𝕊 N−1, for the (N − 1)-sphere 𝕊 N−1 ⊂ ℝ N . If p = 2 these are the classical fractional harmonic maps first considered by Da Lio and Rivière. For p ≠ 2 this is a new energy which has degenerate, non-local Euler-Lagrange equations. They are different from the n/p-harmonic maps introduced by Da Lio and the author, and have to be treated with new arguments, which might be of independent interest for further applications on geometric energies. The main result is Hölder continuity for these maps in the critical case .