Partial regularity for solutions to subelliptic eikonal equations

Abstract

On a bounded domain $\Omega$ in euclidean space ${\mathbb{R}}^n$, we study the homogeneous Dirichlet problem for the eikonal equation associated with a system of smooth vector fields, which satisfies Hörmander's bracket generating condition. We prove that the solution is smooth in the complement of a closed set of Lebesgue measure zero.