Some universal inequalities for Dirichlet eigenvalues of the Laplacian on a Euclidean convex domain

TL;DR

This paper proves two universal inequalities related to the Dirichlet eigenvalues of the Laplacian specifically for convex domains in Euclidean space.

Contribution

It introduces new universal inequalities for Dirichlet eigenvalues on convex Euclidean domains, expanding the theoretical understanding of spectral properties.

Findings

Established two universal inequalities for Dirichlet eigenvalues.

Results apply specifically to convex Euclidean domains.

Advances the theoretical framework of Laplacian eigenvalues.

Abstract

We establish two universal inequalities for Dirichlet eigenvalues of the Laplacian on a Euclidean convex domain.