论文标题
第一个卷曲特征值的最佳凸域
Optimal convex domains for the first curl eigenvalue
论文作者
论文摘要
我们证明存在一个有界的凸域$ω\ subset \ mathbf {r}^3 $固定体积的3 $，该体积最小化了同一体积的所有其他有限的凸域中的第一个正弯曲eigenValue。我们表明，此最佳域不能进行分析，并且如果它足够平滑（例如，$ c^{1,1} $），则不能稳定凸。还介绍了一个均匀的Hölder最佳域（即包含在固定有限域中$ d \ subset \ Mathbf {r}^3 $）的存在结果。
We prove that there exists a bounded convex domain $Ω\subset \mathbf{R}^3$ of fixed volume that minimizes the first positive curl eigenvalue among all other bounded convex domains of the same volume. We show that this optimal domain cannot be analytic, and that it cannot be stably convex if it is sufficiently smooth (e.g., of class $C^{1,1}$). Existence results for uniformly Hölder optimal domains in a box (that is, contained in a fixed bounded domain $D \subset \mathbf{R}^3$) are also presented.
