具有部分BMO系数的非散度型抛物方程的Lorentz估计  

Lorentz Estimates for Nondivergence Parabolic Equations with Partially BMO Coefficients

作　　者：张俊杰 郑神州[2] 于海燕[3] Zhang Junjie;Zheng Shenzhou;Yu Haiyan(College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang 050016;Department of Mathematics,Beijing Jiaotong University,Beijing 100044;College of Mathematics,Inner Mongolia University for Nationalities,Inner Mongolia Tongliao 028043)

机构地区：[1]河北师范大学数学科学学院,石家庄050024 [2]北京交通大学理学院,北京100044 [3]内蒙古民族大学数学学院,内蒙古通辽028043

出　　处：《数学物理学报（A辑）》2019年第6期1405-1420,共16页Acta Mathematica Scientia

基　　金：河北师范大学科研基金(L2019B02);河北省自然科学基金(A2019205218);内蒙古自治区自然科学基金(2018MS01008);内蒙古自治区高等学校科学研究项目(NJZY18164)~~

摘　　要：该文利用"大M不等式原理"证明了非散度型线性抛物方程ut−aij(x,t)Diju(x,t)=f(x,t)强解Hessian矩阵的内部Lorentz估计,其中主项系数aij(x,t)满足一致抛物条件和部分BMO条件,即aij(x,t)关于一个空间变量可测且关于其余变量具有小的BMO半范数.In this paer,we prove an interior Lorentz estimate for Hessian of the strong solutions to nondivergence linear parabolic equations ut−aij(x,t)Diju(x,t)=f(x,t).Here,the leading coefficients aij(x,t)are assumed to be merely measurable in one spatial variable and have small BMO semi-norms with respect to the remaining variables.

关 键 词：非散度型抛物方程 LORENTZ空间 部分BMO 

分 类 号：O175.2[理学—数学]