退化多凸能临界点的正则性和紧凑性

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED Archive for Rational Mechanics and Analysis Pub Date : 2024-11-04 DOI:10.1007/s00205-024-02055-y

André Guerra, Riccardo Tione

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引用次数: 0

摘要

我们研究了二维中能量 \(\int _\Omega g(\det\text {D} u) \,\text {d} x\) 的 Lipschitz 临界点，其中 g 是一个严格的凸函数。我们证明了任何 Lipschitz 临界点的 Jacobian 都是常数，并且近似临界点序列的 Jacobian 都强烈收敛。后一结果特别回答了 Kirchheim、Müller 和 Šverák 于 2003 年提出的一个未决问题。

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Regularity and compactness for critical points of degenerate polyconvex energies

We study Lipschitz critical points of the energy \(\int _\Omega g(\det \text {D} u) \,\text {d} x\) in two dimensions, where g is a strictly convex function. We prove that the Jacobian of any Lipschitz critical point is constant, and that the Jacobians of sequences of approximately critical points converge strongly. The latter result answers, in particular, an open problem posed by Kirchheim, Müller and Šverák in 2003.

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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.