On the Subelliptic Eikonal Equation

Abstract

On a bounded smooth domain, we consider the viscosity solution of the homogeneous Dirichlet problem for the eikonal equation associated with a system of Hörmander’s vector fields. We present some results on the regularity and the structure of the singular support of such a function.

Keywords

• eikonal equation
• degenerate equations
• sub-Riemannian geometry