Regularity of solution maps of differential inclusions under state constraints

Abstract

Consider a differential inclusion under state constraints x'(t) F(t, x(t)), x(t) K, where F is a closed convex, not necessarily bounded set-valued map, which is measurable in t and k(t)-Lipschitz in x (with k(·) L1) and K Rn is a closed set with smooth boundary. ......