Global Lorentz estimates for nonlinear parabolic equations on nonsmooth domains

2017/02/17 by The Anh Bui, Bui, The Anh, Xuan Thinh Duong +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.06202

openalex publication_date 2017/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the nonlinear parabolic equation in the form u_t-\rm div a(D u,x,t)=\rm div (|F|^p-2F) in Ω×(0,T), where T>0 and Ω is a Reifenberg domain. We suppose that the nonlinearity a(ξ,x,t) has a small BMO norm with respect to x and is merely measurable and bounded with respect to the time variable t. In this paper, we prove the global Calderón-Zygmund estimates for the weak solution to this parabolic problem in the setting of Lorentz spaces which includes the estimates in Lebesgue spaces. Our global Calderón-Zygmund estimates extend certain previous results to equations with less regularity assumptions on the nonlinearity a(ξ,x,t) and to more general setting of Lorentz spaces.

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