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

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 $$u_t-\mathrm{div}(A(x,t)\nabla u)=\mathrm{div}(F),$$ 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.

13 pages

Cited by in corpus (1)

• Parabolic weighted Sobolev-Poincaré type inequalities