Viscosity Solutions in Martinet Spaces
Analysis of PDEs
2026-01-28 v1 Differential Geometry
Metric Geometry
Abstract
In this paper, we establish the properties of viscosity solutions in Martinet spaces, which lack both the algebraic group law of Carnot groups and the triangular vector fields of Grushin-type spaces. We then prove the uniqueness of viscosity solutions to strictly monotone elliptic PDEs and to the infinite Laplace equation.
Cite
@article{arxiv.2601.19864,
title = {Viscosity Solutions in Martinet Spaces},
author = {Thomas Bieske and Frederic Bowen},
journal= {arXiv preprint arXiv:2601.19864},
year = {2026}
}