On $(p,q)$-eigenvalues of subelliptic operators on nilpotent Lie groups

TL;DR

This paper investigates the Dirichlet $(p,q)$-eigenvalue problem for subelliptic operators on nilpotent Lie groups, establishing solvability and minimizer existence in a non-commutative setting.

Contribution

It introduces the first results on the solvability and minimizer existence for $(p,q)$-eigenvalues of subelliptic operators on nilpotent Lie groups.

Findings

Proved the solvability of the eigenvalue problem.

Established the existence of a minimizer for the variational problem.

Extended eigenvalue theory to non-commutative subelliptic operators.

Abstract

In the article we study the Dirichlet $(p,q)$-eigenvalue problem for subelliptic non-commutative operators on nilpotent Lie groups. We prove solvability of this eigenvalue problem and existence of the minimizer of the corresponding variational problem.