论文标题
Robin $ p $ -laplacian特征值的估算值
Estimates for Robin $p$-Laplacian eigenvalues of convex sets with prescribed perimeter
论文作者
论文摘要
在本文中，我们证明了$ p $ -laplacian的第一个罗宾特征值的上限，具有正边界参数，以及$ plaplacian $ plaplacian的第一个Robin Eigenvalue的反向Faber-krahn类型不平等的定量版本，带有负面边界参数，convex set in Convex set in Concemencepeperecrecrecrecrecepepers perimeters。 这些证明是基于通过佩恩，魏姆伯格和波利亚引入的内部集合获得的比较参数。
In this paper, we prove an upper bound for the first Robin eigenvalue of the $p$-Laplacian with a positive boundary parameter and a quantitative version of the reverse Faber-Krahn type inequality for the first Robin eigenvalue of the $p$-Laplacian with negative boundary parameter, among convex sets with prescribed perimeter. The proofs are based on a comparison argument obtained by means of inner sets, introduced by Payne, Weimberger and Polya.
