Variational eigenvalues of the subelliptic $p$-Laplacian

TL;DR

This paper establishes a sequence of variational eigenvalues for the subelliptic p-Laplacian using Lusternik-Schnirelman theory, advancing understanding of its spectral properties under Dirichlet boundary conditions.

Contribution

It introduces a novel application of Lusternik-Schnirelman theory to the subelliptic p-Laplacian, proving the existence of an eigenvalue sequence.

Findings

Existence of a nondecreasing eigenvalue sequence

Application of Lusternik-Schnirelman theory to subelliptic operators

Eigenvalues characterized under Dirichlet boundary conditions

Abstract

We use the Lusternik-Schnirelman theory to prove the existence of a nondecreasing sequence of variational eigenvalues for the subelliptic $p$-Laplacian subject to the Dirichlet boundary condition.