Proves uniqueness of viscosity solutions in Martinet spaces, suggesting new insights in PDEs.
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 ∞ (x) -Laplace equation.
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Bieske et al. (2026) studied this question.
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