Shape optimization in compressible liquid crystals

Wenya  Ma; Yihang Hao; Xiangao Liu

doi:10.3934/cpaa.2015.14.1623

Article Contents

2015, Volume 14, Issue 5: 1623-1639. Doi: 10.3934/cpaa.2015.14.1623

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Shape optimization in compressible liquid crystals

1.
College of Information and Management Science, Henan Agricultural University, Zhengzhou
2.
School of Mathematical Sciences, Fudan University, Shanghai

Received: September 30, 2012

Revised: July 31, 2013

Published: August 2015

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Abstract

The shape optimization problem for the profile in compressible liquid crystals is considered in this paper. We prove that the optimal shape with minimal volume is attainable in an appropriate class of admissible profiles which subjects to a constraint on the thickness of the boundary. Such consequence is mainly obtained from the well-known weak sequential compactness method (see [25]).

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Mathematics Subject Classification: Primary: 76N10; Secondary: 35Q35.

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