On the homogeneous Dirichlet problem for the subelliptic eikonal equation

abstract: We consider the subelliptic eikonal equation, i.e. the eikonal equation associated with a family of (real) smooth vector fields satisfying the Hoermander bracket generating condition on a neighborhood of an open bounded set with smooth boundary. We study the regularity and the singularities of the viscosity solution of the homogeneous Dirichlet problem for such an equation.