一类分数阶调和映射迭代算法的收敛性
Convergence of Iterative Algorithm for a Class of Fractional Harmonic Maps
摘要: 基于能量泛函的极小值问题,本文给出了分数阶调和映射方程的一类迭代算法,我们证明了该算法的收敛性。
Abstract: This paper proposes an iterative algorithm for fractional harmonic maps and its convergence is proved.
文章引用:李东雪. 一类分数阶调和映射迭代算法的收敛性[J]. 应用数学进展, 2021, 10(4): 1301-1306. https://doi.org/10.12677/AAM.2021.104139

参考文献

[1] Helein, F. (1990) Regularite des applications faiblement harmoniques entre une surface et une sphere. Comptes Rendus de l’Académie des Sciences—Series I—Mathematics, 311, 519-524.
[2] Lin, F. and Wang, C. (2008) The Analysis of Harmonic Maps and Their Heat Flows. World Scientific Publishing Co. Pte. Ltd., Hackensack, HJ. [Google Scholar] [CrossRef
[3] Riviere, T. (2007) Conservation Laws for Conformally Invariant Variational Problems. Inventiones Mathematicae, 168, 1-22. [Google Scholar] [CrossRef
[4] Da Lio, F. and Riviere, T. (2011) Three-Term Commutator Estimates and the Regularity of 1/2-Harmonic Maps into Spheres. Analysis & PDE, 4, 149-190. [Google Scholar] [CrossRef
[5] Da Lio, F. (2013) Fractional Harmonic Maps into Manifolds in Odd Dimension n > 1. Calculus of Variations and Partial Differential Equations, 48, 421-445. [Google Scholar] [CrossRef
[6] Da Lio, F. (2015) Compactness and Bubble Analysis for 1/2-Harmonic Maps. Annales de l’Institut Henri Poincaré, 32, 201-224. [Google Scholar] [CrossRef
[7] Schikorra, A. (2012) Regularity of n/2-Harmonic Maps into Spheres. Journal of Differential Equations, 252, 1862-1911. [Google Scholar] [CrossRef
[8] Da Lio, F. and Riviere, T. (2011) Sub-Criticality of Non-Local Schrodinger Systems with Antisymmetric Potentials and Applications to Half-Harmonic Maps. Advances in Mathematics, 227, 1300-1348. [Google Scholar] [CrossRef
[9] Schikorra, A., Sire, Y. and Wang, C. (2017) Weak Solutions of Geometric Flows Associated to Integro-Differential Harmonic Maps. Manuscripta Mathematica, 153, 389-402. [Google Scholar] [CrossRef
[10] Alouges, F. (1997) A New Algorithm for Computing Liquid Crystal Stable Configurations: The Harmonic Mapping Case. SIAM Journal on Numerical Analysis, 34, 1708-1726. [Google Scholar] [CrossRef
[11] Bartels, S. (2005) Stability and Convergence of Finite-Element Approximation Schemes for Harmonic Maps. SIAM Journal on Numerical Analysis, 43, 220-238. [Google Scholar] [CrossRef