On the discrete spectrum of Robin Laplacians in conical domains

TL;DR

This paper investigates how geometric properties of conical domains influence whether Robin Laplacians have a finite or infinite number of discrete eigenvalues, providing conditions that determine spectral behavior.

Contribution

It introduces geometric criteria that guarantee finiteness or infiniteness of the discrete spectrum for Robin Laplacians in conical domains.

Findings

Identifies conditions for finite discrete spectrum

Identifies conditions for infinite discrete spectrum

Provides geometric criteria for spectral classification

Abstract

We discuss several geometric conditions guaranteeing the finiteness or the infiniteness of the discrete spectrum for Robin Laplacians on conical domains.