Serrin 问题与 Alexandrov 肥皂泡定理：通过积分恒等式增强稳定性
偏微分方程分析
2017-09-07 v2
摘要
我们考虑关于抗扭刚度的 Serrin 超定问题和 Alexandrov 肥皂泡定理。我们给出了新的积分恒等式，它们展示了这两个问题之间的强类比，并有助于获得对径向对称构型更好的（在某些情况下是最优的）定量估计。肥皂泡定理的估计得益于 Serrin 问题的估计。
引用
@article{arxiv.1708.07392,
title = {Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities},
author = {Rolando Magnanini and Giorgio Poggesi},
journal= {arXiv preprint arXiv:1708.07392},
year = {2017}
}
备注
18 pages. Corrected typos; Remark 4.8 replaced by Theorem 4.8; introduction slightly modified, accordingly