Minimization of Dirichlet energy of j−degree mappings between annuli

IF 1.3 2区 数学 Q1 MATHEMATICS Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-10-09 DOI:10.1016/j.na.2024.113671
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Abstract

Let A and A be circular annuli in the complex plane, and consider the Dirichlet energy integral of j-degree mappings between A and A. We aim to minimize this energy integral. The minimizer is a j-degree harmonic mapping between the annuli A and A, provided it exists. If such a harmonic mapping does not exist, then the minimizer is still a j-degree mapping which is harmonic in AA, and it is a squeezing mapping in its complementary annulus A=AA. This result is an extension of a certain result by Astala et al. (2010).
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环面间 j 度映射的 Dirichlet 能量最小化
假设 A 和 A∗ 是复平面上的圆形环面,并考虑 A 和 A∗ 之间 j 阶映射的 Dirichlet 能量积分。我们的目标是最小化这个能量积分。最小值是环面 A 和 A∗ 之间的 j 度谐波映射,前提是它存在。如果不存在这样的调和映射,那么最小化映射仍然是一个在 A′⊂A 中调和的 j 度映射,并且是其互补环面 A′′=A∖A′ 中的挤压映射。这一结果是对阿斯塔拉等人(2010)的某个结果的扩展。
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来源期刊
CiteScore
3.30
自引率
0.00%
发文量
265
审稿时长
60 days
期刊介绍: Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.
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