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It is a generally shared opinion that significant information about the topology of a bounded domain Ω of a riemannian manifold M is encoded into the properties of the distance, d ∂Ω , from the boundary of Ω. To confirm such an idea we propose an approach based on the invariance of the singular set of the distance function with respect to the generalized… (More)

The minimum time function T (·) of smooth control systems is known to be locally semiconcave provided Petrov's controllability condition is satisfied. Moreover, such a regularity holds up to the boundary of the target under an inner ball assumption. We generalize this analysis to differential inclusions, replacing the above hypotheses with the continuity of… (More)

We study the time optimal control problem with a general target S for a class of differential inclusions that satisfy mild smoothness and control-lability assumptions. In particular, we do not require Petrov's condition at the boundary of S. Consequently, the minimum time function T (·) fails to be locally Lipschitz—never mind semiconcave—near S. Instead of… (More)

In this paper, we study the compactness in L 1 loc of the semigroup (St) t≥0 of entropy weak solutions to strictly convex scalar conservation laws in one space dimension. The compactness of St for each t > 0 was established by P. D. Lax [10]. Upper estimates for the Kolmogorov's ε-entropy of the image through St of bounded sets in L 1 ∩ L ∞ were given by C.… (More)

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