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

[BibTeX]

Submitted Paper

Inserted: 23 may 2017
Last Updated: 25 may 2017

Year: 2017
Doi: https://arxiv.org/abs/1705.07438

ArXiv: 1705.07438 PDF

Abstract:

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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