2016/02/24 by Н. В. Кузнецов, Kuznetsov, Nikolay
Computer Science · Mathematics · #35J05 #35P15 #49R05 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1602.07447
openalex publication_date 2016/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1960, Payne and Weinberger proved that among all domains that lie within a wedge (an angle whose measure is less than or equal to π), and have a given value of a certain integral the circular sector has the lowest fundamental eigenvalue of the Dirichlet Laplacian. Here, it is shown that an analogue of this assertion is true for domains with a cut and for indented domains; that is, for those located in a reflex angle (its measure is between π and 2 π).