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Shape optimization in compressible liquid crystals

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

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