Weighted lorentz estimates for nondivergence linear elliptic equations with partially BMO coefficients

Junjie Zhang; Shenzhou Zheng

doi:10.3934/cpaa.2017043

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2017, Volume 16, Issue 3: 899-914. Doi: 10.3934/cpaa.2017043

This issue Previous Article $L^p$ boundedness for maximal functions associated with multi-linear pseudo-differential operators Next Article Tug-of-war games with varying probabilities and the normalized p(x)-laplacian

Weighted lorentz estimates for nondivergence linear elliptic equations with partially BMO coefficients

Junjie Zhang and
Shenzhou Zheng^,

Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

^* Corresponding author
^* Corresponding author

Received: August 2016

Revised: December 2016

Published: January 2018

The first author is supported by the Fundamental Research Funds for the Central Universities of China grant 2016YJS154, and the second author is supported by NSF of China grant 11371050.

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Abstract

We prove weighted Lorentz estimates of the Hessian of strong solution for nondivergence linear elliptic equations $a_{ij}(x)D_{ij}u(x)=f(x)$. The leading coefficients are assumed to be measurable with respect to one variable and have small BMO semi-norms with respect to the other variables. Here, an approximation method, Lorentz boundedness of the Hardy-Littlewood maximal operators and an equivalent representation of Lorentz norm are employed.

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Mathematics Subject Classification: Primary: 35J15, 35B65; Secondary: 45E30.

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