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

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.