On the first Robin eigenvalue of a class of anisotropic operators

TL;DR

This paper investigates the first eigenvalue of anisotropic p-Laplace operators with Robin boundary conditions, establishing sharp bounds and monotonicity properties related to domain size and boundary function variations.

Contribution

It provides new sharp lower bounds and monotonicity results for the first eigenvalue of anisotropic p-Laplace operators with non-constant Robin boundary conditions.

Findings

Established sharp lower bounds based on domain measure.

Proved monotonicity of the eigenvalue with respect to set inclusion.

Analyzed effects of non-constant boundary function eta on eigenvalues.

Abstract

The paper is devoted to the study of some properties of the first eigenvalue of the anisotropic $p$-Laplace operator with Robin boundary condition involving a function $\beta$ which in general is not constant. In particular we obtain sharp lower bounds in terms of the measure of the domain and we prove a monotonicity property of the eigenvalue with respect the set inclusion.