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

作　　者：TIAN Hong HAO Shuai ZHENG Shenzhou 

机构地区：[1]College of Science,Tianjin University of Technology,Tianjin 300384,China [2]Department of Mathematics,Beijing Jiaotong University,Beijing 100044,China

出　　处：《Journal of Partial Differential Equations》2024年第2期198-234,共37页偏微分方程（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11901429 and 12071021).

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,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.

关 键 词：A higher-order parabolic equation Sobolev spaces with variable exponents partially BMO quasi-norm Reifenberg flat domains log-Hölder continuity 

分 类 号：O17[理学—数学]