Calculus of Variations and Geometric Measure Theory
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Q. H. Nguyen

Gradient weighted norm inequalities for very weak solutions of linear parabolic equations with BMO coefficients

created by nguyen on 23 May 2017
modified on 25 May 2017


Submitted Paper

Inserted: 23 may 2017
Last Updated: 25 may 2017

Year: 2017

ArXiv: 1705.07438 PDF


In this paper, we prove the Lorentz space $L^{q,p}$-estimates for gradients of very weak solutions to the linear parabolic equations with $\mathbf{A}_q$-weights $$ut-\operatorname{div}(A(x,t)\nabla u)=\operatorname{div}(F),$$ in a bounded domain $\Omega\times (0,T)\subset\mathbb{R}^{N+1}$, where $A$ has a small mean oscillation, and $\Omega$ is a Lipchistz domain with a small Lipschitz constant.

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