Partial Hölder regularity for asymptotically convex functionals with borderline double-phase growth

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-02-12 DOI:10.1002/mana.202400388

Wenrui Chang, Shenzhou Zheng

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引用次数: 0

Abstract

We study partial Hölder regularity of the local minimizers $u \in W_{loc}^{1, 1} (Ω; R^{N})$ with $N \geq 1$ to the integral functional $\int_{Ω} F (x, u, D u) d x$ in a bounded domain $Ω \subset R^{n}$ for $n \geq 2$ . Under the assumption of asymptotically convex to the borderline double-phase functional

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我们研究了局部最小值 u∈ W loc 1 , 1 ( Ω ; R N ) $u\in W_{mathrm{loc}}^{1,1}(\Omega;{\mathbb {R}^N})$ N ≥ 1 $N\ge 1$ 的积分函数∫ Ω F ( x , u , D u ) d x $\int _\Omega F(x,u,Du)\,dx$ 在 n ≥ 2 $n\ge 2$ 的有界域 Ω ⊂ R n $\Omega \子集 \mathbb {R}^n$ 中的部分赫尔德正则性。在近似凸向边界双相函数的假设下

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index