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

2017/05/21 by Nguyen, Quoc-Hung
#Analysis of PDEs (math.AP) #FOS: Mathematics #primary 35K59 #secondary 42B37

paper · doi:10.48550/arxiv.1705.07438

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 A_q-weights u_t-div(A(x,t)∇ u)=div(F), in a bounded domain Ω× (0,T)⊂ℝ^N+1, where A has a small mean oscillation, and Ω is a Lipchistz domain with a small Lipschitz constant.

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