Wm,p(t,x)-Estimate for a Class of Higher-Order Parabolic Equations with Partially BMO Coefficients

被引:0
|
作者
Tian, Hong [1 ]
Hao, Shuai [1 ]
Zheng, Shenzhou [2 ]
机构
[1] Tianjin Univ Technol, Coll Sci, Tianjin 300384, Peoples R China
[2] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China
来源
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS | 2024年 / 37卷 / 02期
基金
中国国家自然科学基金;
关键词
A higher-order parabolic equation; Sobolev spaces with variable exponents; partially BMO quasi-norm; Reifenberg flat domains; log-Ho<spacing diaeresis>lder continuity; ELLIPTIC-OPERATORS; SYSTEMS; REGULARITY; INTEGRABILITY; VMO;
D O I
10.4208/jpde.v37.n2.6June2024
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove a global estimate in the Sobolev spaces with variable exponents to the solution of a class of higher-order divergence parabolic equations with measurable coefficients over the non-smooth domains. Here, it is mainly assumed that the coefficients are allowed to be merely measurable in one of the spatial variables and have a small BMO quasi-norm in the other variables at a sufficiently small scale, while the boundary of the underlying domain belongs to the so-called Reifenberg flatness. This is a natural outgrowth of Dong-Kim-Zhang's papers [1,2] from the W-m,W-p-regularity to the W (m,p(t, x))-regularity for such higher-order parabolic equations with merely measurable coefficients with Reifenberg flat domain which is beyond the Lipschitz domain with small Lipschitz constant.
引用
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页码:198 / 234
页数:37
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