Existence and uniqueness of variational solution to the Neumann problem for the pth sub-Laplacian associated to a system of H\"ormander vector fields

TL;DR

This paper proves the existence and uniqueness of variational solutions for a nonlinear Neumann boundary problem involving the p-th sub-Laplacian linked to H"ormander vector fields, advancing understanding in sub-Riemannian analysis.

Contribution

It establishes the first rigorous proof of existence and uniqueness for this class of nonlinear boundary value problems in the context of H"ormander vector fields.

Findings

Existence of variational solutions is confirmed.

Uniqueness of solutions is established.

Results extend the theory of sub-Laplacians to nonlinear Neumann problems.

Abstract

We establish the existence and uniqueness of variational solution to the nonlinear Neumann boundary problem for the $p^{th}$-Sub-Laplacian associated to a system of H\"ormander vector fields