On the regularity near the boundary of viscosity solutions of eikonal equations

Abstract We consider a non-characteristic boundary value problem for equations of eikonal type and we show that, near the boundary, the viscosity solution inherits the regularity of the data. As a consequence, we slightly improve the results in [1] on the structure of the cut-locus of a class of distance functions. Keywords: Viscosity solutions, Eikonal equation, Cut-locus, Analytic regularity