About symmetry in partially hinged composite plates

TL;DR

This paper investigates symmetry and monotonicity properties of eigenfunctions in partially hinged composite plates, using Green functions and polarization techniques, and introduces a new boundary lemma supported by numerical results.

Contribution

It provides new insights into eigenfunction symmetry in composite plates and introduces a Hopf-type boundary lemma for the associated operator.

Findings

Eigenfunctions exhibit symmetry and monotonicity properties.

Green function analysis supports symmetry results.

Numerical results validate theoretical findings.

Abstract

We consider a partially hinged composite plate problem and we investigate qualitative properties, e.g. symmetry and monotonicity, of the eigenfunction corresponding to the density minimizing the first eigenvalue. The analysis is performed by showing related properties of the Green function of the operator and by applying polarization with respect to a fixed plane. As a by-product of the study, we obtain a Hopf type boundary lemma for the operator having its own theoretical interest. The statements are complemented by numerical results.