二维静态 Q 值映射的内部正则性

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2024-07-22 DOI:10.1007/s00205-024-02011-w

Jonas Hirsch, Luca Spolaor

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引用次数: 0

摘要

我们证明了相对于 Dirichlet 能量的外部和内部变化都是静止的二维 Q 值映射是荷尔德连续的，并且其奇异集的维度最多为一。在证明过程中，我们建立了等价连续映射的强集中-紧凑性定理，这些映射只在外变化方面是静止的，而且在各个维度上都成立。

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Interior Regularity for Two-Dimensional Stationary Q-Valued Maps

We prove that 2-dimensional Q-valued maps that are stationary with respect to outer and inner variations of the Dirichlet energy are Hölder continuous and that the dimension of their singular set is at most one. In the course of the proof we establish a strong concentration-compactness theorem for equicontinuous maps that are stationary with respect to outer variations only, and which holds in every dimensions.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.