Proceedings of the Centre for Mathematics and its Applications

Separation of gradient Young measures and the BMO

Kewei Zhang

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Abstract

Let $K = \{A,B} \subset M^{Nxn$ with rank$(A − B) \gt 1$ and $\Omega \subset \mathbbR^n$ be a bounded arcwise connected Lipschitz domain. We show that there is a direct estimate of the size of the $\epsilon$-neighborhood $K_\epsilon$ of $K$ such that $K_\epsilon = \barB_\epsilon(A) \bigcup \barB_\epsilon(B)$ separates gradient Young measures, that is, if $(u_j) \subset W^{1,1}(\Omega, \mathbbR^N)$ is bounded and $\int_\Omega$ dist$(Du_j, K_\epsilon)dx \rightarrow 0$ as $j \rightarrow \infty$, then up to a subsequence, either $\int_Omega dist(DU_j, \barB_epsilon(A))dx \rightarrow 0$ or $\int_Omega dist(Du_j, \barB_epsilon(B))dx \rightarrow 0$.

Article information

Source
International Conference on Harmonic Analysis and Related Topics. Xuan Thinh Duong and Alan Pryde, eds. Proceedings of the Centre for Mathematics and its Applications, v. 41. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 2003), 161-169

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416322435

Mathematical Reviews number (MathSciNet)
MR1994523

Zentralblatt MATH identifier
1104.49016

Citation

Zhang, Kewei. Separation of gradient Young measures and the BMO. International Conference on Harmonic Analysis and Related Topics, 161--169, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 2003. https://projecteuclid.org/euclid.pcma/1416322435


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