具有部分BMO系数的非散度型抛物方程的Lorentz估计

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1405-1420.

具有部分BMO系数的非散度型抛物方程的Lorentz估计

张俊杰¹(),郑神州²(),于海燕³()

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

收稿日期:2018-06-28 出版日期:2019-12-26 发布日期:2019-12-28
作者简介:张俊杰, E-mail: junjiezhang@hebtu.edu.cn|郑神州, E-mail: shzhzheng@bjtu.edu.cn|于海燕, E-mail: jiechy@163.com
基金资助:
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)

Lorentz Estimates for Nondivergence Parabolic Equations with Partially BMO Coefficients

Junjie Zhang¹(),Shenzhou Zheng²(),Haiyan Yu³()

¹ College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016
² Department of Mathematics, Beijing Jiaotong University, Beijing 100044
³ College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia Tongliao 028043

Received:2018-06-28 Online:2019-12-26 Published:2019-12-28
Supported by:
the Science Foundation of Hebei Normal University(L2019B02);the Natural Science Foundation of Hebei Province(A2019205218);the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(2018MS01008);the Science Research Program of Institution of Higher Education at Universities of Inner Mongolia Autonomous Region(NJZY18164)

摘要/Abstract

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

$ {{u}_{t}}-{{a}_{ij}}(x,t){{D}_{ij}}u(x,t)=f(x,t) $

强解Hessian矩阵的内部Lorentz估计，其中主项系数a_ij（x，t）满足一致抛物条件和部分BMO条件，即a_ij（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.

关键词: 非散度型抛物方程, Lorentz空间, 部分BMO

Abstract:

In this paer, we prove an interior Lorentz estimate for Hessian of the strong solutions to nondivergence linear parabolic equations u_t -a_ij(x, t)D_iju(x, t)=f(x, t). Here, the leading coefficients a_ij(x, t) are assumed to be merely measurable in one spatial variable and have small BMO semi-norms with respect to the remaining variables.

Key words: Nondivergence parabolic equations, Lorentz spaces, Partially BMO

中图分类号:

O175.2

张俊杰,郑神州,于海燕. 具有部分BMO系数的非散度型抛物方程的Lorentz估计[J]. 数学物理学报, 2019, 39(6): 1405-1420.

Junjie Zhang,Shenzhou Zheng,Haiyan Yu. Lorentz Estimates for Nondivergence Parabolic Equations with Partially BMO Coefficients[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1405-1420.

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