论文标题
反向Faber-Krahn不平等的$ p $ -laplacian在双曲线空间中
Reverse Faber-Krahn inequality for the $p$-Laplacian in Hyperbolic space
论文作者
论文摘要
在本文中，我们研究了$ p $ laplace运算符的第一个特征值的形状优化问题，具有混合的neumann-dirichlet边界条件在双曲线空间中的多连接域上。确切地说，我们确定在给定体积的所有乘数域中，并规定了convex dirichlet边界（内边界）的$（n-1）$ - QuermassIntegral，同心环形区域产生最大的第一个特征值。我们还针对双曲线空间中凸形域的外部平行组得出了Nagy的类型不等式。
In this paper, we study the shape optimization problem for the first eigenvalue of the $p$-Laplace operator with the mixed Neumann-Dirichlet boundary conditions on multiply-connected domains in hyperbolic space. Precisely, we establish that among all multiply-connected domains of a given volume and prescribed $(n-1)$-th quermassintegral of the convex Dirichlet boundary (inner boundary), the concentric annular region produces the largest first eigenvalue. We also derive Nagy's type inequality for outer parallel sets of a convex domain in the hyperbolic space.
