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Regularity estimates for higher order elliptic systems on Reifenberg flat domains

Authors: 

The Anh Bui, Xuan Thinh Duong, Xuan Truong Le*

Source title: 
Journal of Differential Equations, 261(10): 5637-5669, 2016 (ISI)
Academic year of acceptance: 
2016-2017
Abstract: 

Consider a higher order elliptic system

Cong%20thuc%20bai%20a%20Truong%20-%20Regularity%20estimates.gif

 

 

for all i=1,…,N with N∈N+, and all multi-indices |α|=mi, |β|=mj with mi∈N+ for all i=1,…,N, and the standard summation notation is understood. We assume that the leading coefficients cong%20thuc%202.gif have small BMO norms and the domain Ω⊂Rn is open, bounded and flat in the Reifenberg's sense. This article is to prove the regularity estimates of this system in weighted Lorentz spaces and in Lorentz–Morrey spaces. Our results require weak assumptions on the regularity of the coefficients cong%20thuc%202.gif and the boundary ∂Ω, and they are new even for scalar higher order elliptic equations