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

Article type: Research Article

Authors: Thanh Bui, Le Trong^{a; b} | Nguyen, Quoc-Hung^{c; *}

Affiliations: [a] Faculty of Mathematics and Computer Science, University of Science, 227 Nguyen Van Cu, D. 5, Ho Chi Minh City, Vietnam | [b] Vietnam National University, Ho Chi Minh City, Vietnam. E-mail: bltthanh@hcmus.edu.vn | [c] ShanghaiTech University, 393 Middle Huaxia Road, Pudong, Shanghai, 201210, China. E-mail: qhnguyen@shanghaitech.edu.cn

Correspondence: [*] Corresponding author. E-mail: qhnguyen@shanghaitech.edu.cn.

Abstract: In this paper, we give a short proof of the Lorentz estimates for gradients of very weak solutions to the linear parabolic equations with the Muckenhoupt class Aq-weights ut−div(A(x,t)∇u)=div(F), in a bounded domain Ω×(0,T)⊂RN+1, where A has a small mean oscillation, and Ω is a Lipchistz domain with a small Lipschitz constant.

Keywords: Quasilinear parabolic equations, maximal potential, Reifenberg flat domain

DOI: 10.3233/ASY-211693

Journal: Asymptotic Analysis, vol. 127, no. 4, pp. 339-353, 2022