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- W4308161911 abstract "Let $mu>0$ be a fixed constant, and we prove that minimizers to the following energy functional begin{align*} E_f(u,Omega):=int_{Omega}|nabla u|^2+mu P(Omega) end{align*}exist among pairs $(Omega,u)$ such that $Omega$ is an $M$-uniform domain with finite perimeter and fixed volume, and $u in H^1(Omega,mathbb{S}^2)$ with $u =nu_{Omega}$, the measure-theoretical outer unit normal, almost everywhere on the reduced boundary of $Omega$. The uniqueness of optimal configurations in various settings is also obtained. In addition, we consider a general energy functional given by begin{align*} E_f(u,Omega):=int_{Omega} |nabla u(x)|^2 ,dx + int_{partial^* Omega} fbig(u(x)cdot nu_{Omega}(x)big) ,dmathcal{H}^2(x), end{align*}where $partial^* Omega$ is the reduced boundary of $Omega$ and $f$ is a convex positive function on $mathbb R$. We prove that minimizers of $E_f$ also exist among $M$-uniform outer-minimizing domains $Omega$ with fixed volume and $u in H^1(Omega,mathbb{S}^2)$." @default.
- W4308161911 created "2022-11-08" @default.
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- W4308161911 date "2022-11-02" @default.
- W4308161911 modified "2023-10-17" @default.
- W4308161911 title "On a variational problem of nematic liquid crystal droplets" @default.
- W4308161911 doi "https://doi.org/10.48550/arxiv.2211.01218" @default.
- W4308161911 hasPublicationYear "2022" @default.
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