Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity

TL;DR

This paper explores open problems and partial solutions in spectral optimization, focusing on measure, torsional rigidity, and the first Dirichlet eigenvalue, contributing to the understanding of these mathematical properties.

Contribution

It introduces new open problems and provides partial results in the area of spectral optimization involving measure, torsional rigidity, and eigenvalues.

Findings

Identification of open problems in spectral optimization

Partial results on measure and torsional rigidity

Insights into the first Dirichlet eigenvalue

Abstract

We present some open problems and obtain some partial results for spectral optimization problems involving measure, torsional rigidity and first Dirichlet eigenvalue.