A shape optimization problem for Steklov eigenvalues in oscillating domains

TL;DR

This paper investigates how nonlinear Steklov eigenvalues behave asymptotically when the domain undergoes irregular but smooth perturbations, contributing to the understanding of optimal shape design in oscillating domains.

Contribution

It provides new insights into the asymptotic analysis of nonlinear Steklov eigenvalues under domain perturbations, advancing optimal shape design theory.

Findings

Asymptotic behavior characterized for perturbed domains

Insights into optimal design for oscillating geometries

Extension of Steklov eigenvalue analysis to irregular domains

Abstract

In this paper we study the asymptotic behavior of some optimal design problems related to nonlinear Steklov eigenvalues, under irregular (but diffeomorphic) perturbations of the domain.