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

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 ${\mathbb{R}}^2$.

19 pages, 4 figures, and comments are welcome. Revisions have been made to Theorem 1.7 and Remark 1.8 of the previous version v1