Regularity estimates for higher order elliptic systems on Reifenberg flat domains

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• 作者：The Anh Bui^a ; ^{the.bui@mq.edu.au" class="auth_mail" title="E-mail the corresponding author} ; ^{bt_anh80@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Xuan Thinh Duong^a ; ^{xuan.duong@mq.edu.au" class="auth_mail" title="E-mail the corresponding author} ; Xuan Truong Le^b ; ^c ; ^{lexuantruong@tdt.edu.vn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J48 ; 35B65
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：261
• 期：10
• 页码：5637-5669
• 全文大小：417 K

文摘

Consider a higher order elliptic system for all i=1,…,N$i=1,\dots ,N$ with N∈N₊$N\in {\mathbb{N}}_{+}$, and all multi-indices 803451c" title="Click to view the MathML source">|α|=m_i$|\alpha |=m_i$, |β|=m_j$|\beta |=m_j$ with 80efc4eaa95" title="Click to view the MathML source">m_i∈N₊$m_i\in {\mathbb{N}}_{+}$ for all i=1,…,N$i=1,\dots ,N$, and the standard summation notation is understood. We assume that the leading coefficients $a_{ij}^{\alpha \beta }(x)$ have small BMO norms and the domain 8516168a1bb26788929f9a15e233dc3" title="Click to view the MathML source">Ω⊂Rⁿ$\mathrm{\Omega }\subset {\mathbb{R}}^n$ 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 $a_{ij}^{\alpha \beta }(x)$ and the boundary ∂Ω, and they are new even for scalar higher order elliptic equations.