Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (6): 1405-1420.

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Lorentz Estimates for Nondivergence Parabolic Equations with Partially BMO Coefficients

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

  1. 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)

Abstract:

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.

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

CLC Number: 

  • O175.2
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