A shape optimization problem for the first mixed Steklov-Dirichlet eigenvalue

TL;DR

This paper investigates a shape optimization problem for the first mixed Steklov-Dirichlet eigenvalue in domains bounded by two balls within two-point homogeneous spaces, providing a geometric proof inspired by Newton's shell theorem.

Contribution

It introduces a novel geometric proof for the optimization problem related to mixed Steklov-Dirichlet eigenvalues in specific symmetric spaces.

Findings

Identification of optimal domain shapes for the eigenvalue problem

Development of a geometric proof based on Newton's shell theorem

Extension of eigenvalue optimization results to two-point homogeneous spaces

Abstract

We consider a shape optimization problem for the first mixed Steklov-Dirichlet eigenvalues of domains bounded by two balls in two-point homogeneous space. We give a geometric proof which is motivated by Newton's shell theorem