Viscosity solutions in Martinet spaces

In this paper, we establish the properties of viscosity solutions in Martinet spaces, which are sub-Riemannian spaces that 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, to the infinite Laplace equation, and to the $${\mathbf {\infty (x)}}$$ -Laplace equation.