论文标题
罗宾扭转问题的刚性结果
A Rigidity Result for the Robin Torsion Problem
论文作者
论文摘要
令$ω\ subset \ mathbb {r}^2 $为开放，有限和Lipschitz设置。我们考虑与罗宾边界条件相关的拉普拉斯操作员的扭转问题。在这种情况下，我们研究了Talenti-Type比较中的平等案例，在Arxiv：1909.11950中证明。我们证明，仅当$ω$是磁盘而扭转函数$ u $是径向的情况下，才能实现平等。
Let $Ω\subset \mathbb{R}^2$ be an open, bounded and Lipschitz set. We consider the torsion problem for the Laplace operator associated to $Ω$ with Robin boundary conditions. In this setting, we study the equality case in the Talenti-type comparison, proved in arXiv:1909.11950. We prove that the equality is achieved only if $Ω$ is a disk and the torsion function $u$ is radial.
