A weak compactness result for critical elliptic systems of n-harmonic type

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• 作者：Michał Miśkiewicz ^{M.Miskiewicz@mimuw.edu.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：p-Harmonic maps ; Uhlenbeck decomposition ; Concentration-compactness ; Compensated compactness
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 July 2016
• 年：2016
• 卷：439
• 期：1
• 页码：370-384
• 全文大小：384 K

文摘

The paper considers systems of the form on a bounded domain in Rⁿ${\mathbb{R}}^n$ with u∈W^1,n$u\in W^{1,n}$, a matrix Ω∈Lⁿ$\mathrm{\Omega }\in L^n$ (depending on u) and some additional structural assumptions on Ω. We prove that if a sequence of solutions of the above system converges weakly, the limit itself is also a solution. The class of systems considered includes the n-harmonic system and the presented reasoning is a generalization of C. Wang's proof for n-harmonic maps.