Global Marcinkiewicz estimates for nonlinear parabolic equations with nonsmooth coefficients

2017/02/17 by Bui, The Anh, Xuan Thinh Duong, Duong, Xuan Thinh
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.06200

openalex publication_date 2017/02/17 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Consider the parabolic equation with measure data \ \beginaligned amp;u_t-\rm div a(D u,x,t)=μamp;inamp; Ω_T, amp;u=0 amp;onamp; ∂_pΩ_T, \endaligned. where Ω is a bounded domain in ℝⁿ, Ω_T=Ω× (0,T), ∂_pΩ_T=(∂Ω× (0,T))∪ (Ω×\0\), and μ is a signed Borel measure with finite total mass. Assume that the nonlinearity \bf a satisfies a small BMO-seminorm condition, and Ω is a Reifenberg flat domain. This paper proves a global Marcinkiewicz estimate for the SOLA (Solution Obtained as Limits of Approximation) to the parabolic equation.

Citations

• Solution of the Plateau problem for m-dimensional surfaces of varying topological type

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