Improved regularity for a Hessian-dependent functional

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-05-01 DOI:10.1090/proc/16894

Vincenzo Bianca, Edgard Pimentel, José Urbano

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引用次数: 0

Abstract

We prove that minimizers of the L d L^{d} -norm of the Hessian in the unit ball of R d \mathbb {R}^d are locally of class C 1 , α C^{1,\alpha } . Our findings extend previous results on Hessian-dependent functionals to the borderline case and resonate with the Hölder regularity theory available for elliptic equations in double-divergence form.

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改进依赖于黑森函数的正则性

我们证明，在 R d \mathbb {R}^d 的单位球中，Hessian 的 L d L^{d} 准则的最小值局部属于 C 1 类，α C^{1,\alpha }。 .我们的发现将之前关于依赖于 Hessian 的函数的结果扩展到了边界情况，并与双发散形式椭圆方程的赫尔德正则性理论产生了共鸣。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.