Spectral isoperimetric inequalities for a class of mixed eigenvalue problems of the Laplacian on triangles and trapezoids

2025/08/15 by Chen, Ruifeng, Mao, Jing
Mathematics · #35J15 #35P15 #49Jxx #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2508.11135

openalex publication_date 2025/08/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

In this paper, under suitable geometric constraints, we have successfully obtained characterizations for the extremum values of the functional of mixed eigenvalues of the Laplacian on triangles (or trapezoids) in the Euclidean plane ℝ².

Citations

• Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacian
• On mixed Dirichlet-Neumann eigenvalues of triangles

Related

• Isoperimetric inequalities for eigenvalues of triangles
• Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions
• An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane
• Isoperimetric Bounds for Eigenvalues of the Wentzell-Laplace, the Laplacian and a biharmonic Steklov Problem
• Isoperimetric and Universal Inequalities for Eigenvalues