量化传奇和最小值的规律性

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2024-07-29 DOI:10.1007/s00205-024-02008-5

Cristiana De Filippis, Lukas Koch, Jan Kristensen

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引用次数: 0

摘要

我们通过凸对偶性引入了变分问题中非均匀椭圆性的新量化，并证明了可能退化函数的矢量值最小化的高微分性和 2d 平滑性结果。我们的框架涵盖了凸、各向异性多项式作为原型模型实例--特别是，我们以基本最优的方式改进了 Marcellini 的原始结果（Marcellini 在 Arch Rat Mech Anal 105:267-284, 1989）。

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Quantified Legendreness and the Regularity of Minima

We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and 2d-smoothness results for vector valued minimizers of possibly degenerate functionals. Our framework covers convex, anisotropic polynomials as prototypical model examples—in particular, we improve in an essentially optimal fashion Marcellini’s original results (Marcellini in Arch Rat Mech Anal 105:267–284, 1989).

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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.