The principal eigenfunction of the Dirichlet Laplacian with prescribed numbers of critical points on the upper half of a topological torus

2021/09/07 by Kamalia, Putri Zahra, Sakaguchi, Shigeru
#35J05 #35J25 #47A75 #58J37 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.02829

Abstract

We consider the principal eigenvalue problem for the Laplace-Beltrami operator on the upper half of a topological torus under the Dirichlet boundary condition. We present a construction of the upper half of a topological torus that admits the principal eigenfunction having exact numbers of critical points. Furthermore, we manage to identify the locations of all the critical points of the principal eigenfunction explicitly.

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