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168体育在线:20221215 王长友 On Variational Problems of Nematic Liquid Crystal Droplets

$inf\{ E(u, U)=1/2\int_U |Du|^2 +\int_{\partial U}f(<u,\nu_U>) \},$

among all open sets $U \subset B_R$ with fixed volume V, and all Sobolev maps $u\in H^1(U, S^2)$.

I will present some results on the existence of minimizers, and the uniqueness of optimal liquid crystal droplets with homeotropic anchoring condition for the director $u$ among certain types of open sets

$U$.

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