An isoperimetric inequality for a biharmonic Steklov problem

TL;DR

This paper proves that among all bounded $C^{1}$ Euclidean domains with fixed volume, the ball maximizes the first positive eigenvalue for a specific biharmonic Steklov problem, establishing a geometric inequality.

Contribution

It establishes an isoperimetric inequality for the first positive eigenvalue in a biharmonic Steklov problem, identifying the ball as the maximizer among fixed measure domains.

Findings

The ball maximizes the first positive eigenvalue among fixed measure domains.

The result applies to $C^{1}$ bounded Euclidean domains.

The paper extends isoperimetric inequalities to biharmonic Steklov problems.

Abstract

For the biharmonic Steklov eigenvalue problem considered in this paper, we show that among all bounded Euclidean domains of class $C^{1}$ with fixed measure, the ball maximizes the first positive eigenvalue.