Singular subelliptic equations and Sobolev inequalities on nilpotent Lie groups

TL;DR

This paper investigates singular subelliptic p-Laplace equations and Sobolev inequalities on nilpotent Lie groups, establishing solvability, minimizer existence, and best constants in these inequalities.

Contribution

It proves the solvability of singular subelliptic p-Laplace equations and the existence of best constants in Sobolev inequalities on nilpotent Lie groups, advancing understanding in this area.

Findings

Proved solvability of singular subelliptic p-Laplace equations.

Established existence of minimizers for associated variational problems.

Determined best constants in Sobolev inequalities on nilpotent Lie groups.

Abstract

In this article we study singular subelliptic $p$-Laplace equations and best constants in Sobolev inequalities on nilpotent Lie groups. We prove solvability of these subelliptic $p$-Laplace equations and existence of the minimizer of the corresponding variational problem. It leads to existence of the best constant in the corresponding $(q,p)$-Sobolev inequality, $0<q<1$, $1<p<\nu$.