Rectifiability results for singular and conjugate points of optimal exit time problems

We consider the value function V of optimal control problems with exit time. Under suitable assumptions, through the study of the conjugate points, we prove that the closure of the singular set of V is rectifiable. Moreover, a sharper Hausdorff estimate is given on the set of the conjugate nonsingular points.  2002 Elsevier Science (USA). All rights reserved.