一类A-调和方程弱解的正则性

兰州理工大学学报 ›› 2026, Vol. 52 ›› Issue (1): 158-163.

一类A-调和方程弱解的正则性

刘文如, 吕月明^*

哈尔滨理工大学理学院, 黑龙江哈尔滨 150080

收稿日期:2024-01-09 出版日期:2026-02-28 发布日期:2026-03-05
通讯作者: 吕月明(1984-),女,黑龙江哈尔滨人,副教授.Email:yueminglu@hrbust.edu.cn
基金资助:
国家自然科学基金(11901140),黑龙江省自然科学基金联合引导项目(LH2022A015),黑龙江省高等教育教学改革项目(SJGPYXM012)

The regularity of weak solutions for a class of A-harmonic equations

LIU Wen-ru, LU Yue-ming

College of Science, Harbin University of Science and Technology, Harbin 150080, China

Received:2024-01-09 Online:2026-02-28 Published:2026-03-05

摘要/Abstract

摘要： 为了研究一类椭圆型调和方程的解在Besov空间的梯度估计,确定合适的算子A与算子B的结构条件;引入向量场函数,并利用该函数与A算子的结构条件得到拟单调性不等式;借助有限差分方法, Hölder不等式,Young不等式估计梯度的增长情况;利用嵌入定理,得到了解的梯度在Besov空间中的正则性结果.

关键词: A-调和方程, Hölder不等式, Young不等式, 正则性

Abstract: To study the gradient estimations of solutions for a class of elliptic harmonic equations in Besov space, appropriate structural conditions for operator A and operator B were established first. Then, a vector field function was introduced, in conjunction with the structural conditions of operator A, to derive a quasi-monotonicity inequality. The growth of the gradient was estimated by employing finite difference methods, Hölder’s inequality, and Young’s inequality. Finally, the regularity results for the gradient of the solutions in the Besov space were obtainedby utilizing embedding theorems.

Key words: A-harmonic equation, Hölder inequality, Young inequality, regularity

中图分类号:

O152.5

刘文如, 吕月明. 一类A-调和方程弱解的正则性[J]. 兰州理工大学学报, 2026, 52(1): 158-163.

LIU Wen-ru, LU Yue-ming. The regularity of weak solutions for a class of A-harmonic equations[J]. Journal of Lanzhou University of Technology, 2026, 52(1): 158-163.

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