On the first Dirichlet Laplacian eigenvalue of regular polygons

Kodai Mathematical Journal

Carlo Nitsch¹ 

[1] Mathematisches Institut Universität zu Köln

关键词: First Dirichlet Laplacian eigenvalue;    Isoperimetric inequality;    Shape derivative;    Eigenvalues on polygons;   

DOI  :  10.2996/kmj/1414674611

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(21)The Faber-Krahn inequality in R2 states that among all open bounded sets of given area the disk minimizes the first Dirichlet Laplacian eigenvalue. It was conjectured in [1] that for all N ≥ 3 the first Dirichlet Laplacian eigenvalue of the regular N-gon is greater than the one of the regular (N + 1)-gon of same area. This natural idea is suggested by the fact that the shape becomes more and more "rounded" as N increases and it is supported by clear numerical evidences. Aiming to settle such a conjecture, in this work we investigate possible ways to estimate the difference between eigenvalues of regular N-gons and (N + 1)-gons.

【 授权许可】

Unknown