非齐次椭圆障碍问题弱解梯度的局部 Besov 估计

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2225-2238.

非齐次椭圆障碍问题弱解梯度的局部 Besov 估计

要佳慧, 佟玉霞^*()

华北理工大学理学院河北唐山 063210

收稿日期:2025-05-13 修回日期:2025-10-17 出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 佟玉霞 E-mail:tongyuxia@126.com
基金资助:
华北理工大学研究生创新项目(2026S28)

Local Besov Estimates for the Gradient of Weak Solutions to Nonhomogeneous Elliptic Obstacle Problems

Jiahui Yao, Yuxia Tong^*()

College of Science, North China University of Science and Technology, Hebei Tangshan 063210

Received:2025-05-13 Revised:2025-10-17 Online:2026-12-26 Published:2026-08-14
Contact: Yuxia Tong E-mail:tongyuxia@126.com
Supported by:
Graduate Student Innovation Fund of North China University of Science and Technology(2026S28)

摘要/Abstract

摘要：

该文研究了与非齐次椭圆方程相对应的障碍问题, 通过建立适当的容许函数, 并利用变分不等式、$N$-函数的 Young 不等式和有限差分法等技巧, 建立了椭圆障碍问题弱解梯度在有界开区域上的局部 Besov 估计.

关键词: 障碍问题, 弱解, Besov 估计, 有限差分

Abstract:

This paper studies the obstacle problem corresponding to non-homogeneous elliptic equations. By establishing appropriate admissible functions and using techniques such as variational inequalities, Young's inequality for $N$-functions, and the finite difference method, a local Besov estimate for the gradient of the weak solution of the elliptic obstacle problem in a bounded open domain is established.

Key words: obstacle problem, weak solution, Besov estimate, finite difference

中图分类号:

O175.25

要佳慧, 佟玉霞. 非齐次椭圆障碍问题弱解梯度的局部 Besov 估计[J]. 数学物理学报, 2026, 46(6): 2225-2238.

Jiahui Yao, Yuxia Tong. Local Besov Estimates for the Gradient of Weak Solutions to Nonhomogeneous Elliptic Obstacle Problems[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2225-2238.

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