改进依赖于黑森函数的正则性

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

摘要

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。

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Improved regularity for a Hessian-dependent functional

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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