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

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 $\mathbb{R}^2$.

Publication Details

Journal
ArXiv.org
Published
2025-08-15
Primary Topic
Geological and Geochemical Analysis
Type
article
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article

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

ArXiv.org
Geological and Geochemical Analysis
article

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

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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 $\mathbb{R}^2$.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 46%
Geological and Geochemical Analysis
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Spectral isoperimetric inequalities for a class of mixed eigenvalue problems of the Laplacian on triangles and trapezoids · ArXiv.org (2025) | TGRS Research Map | TGRS