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Upper semicontinuous differential inclusions without convexity
We prove existence of solutions to the Cauchy problem for the differential inclusion x E A(x) , when A is cyclically monotone and upper semicontinuous.
Variational Inequalities and Regularity Properties of Closed Sets in Hilbert Spaces
Some properties of closed sets which generalize concepts of Convex Analysis are compared and characterized. Some of them have a global character and are concerned with controlling the lack ofExpand
The Sweeping Processes without Convexity
We study the sweeping processes in a Hilbert space which are generated by a closed not necessarily convex moving set. A technique is developed, based on measurability properties of normal cones, inExpand
On the Structure of the Minimum Time Function
We show that $hypo(T)$ is $\varphi$-convex, i.e. twice differentiable and satisfies some further regularity properties. Expand
Sweeping by a continuous prox-regular set $
Abstract The evolution problem known as sweeping process is considered for a class of nonconvex sets called prox-regular (or ϕ -convex). Assuming, essentially, that such sets contain in the interiorExpand
The Minimum Time Function for the Controlled Moreau's Sweeping Process
We consider the problem of reaching a target $S$ within the graph of $C$ subject to the differential inclusion of a Lipschitz set-valued map with closed and (mildly non-)convex values. Expand
On the Minimum Time Function Around the Origin
We deal with finite dimensional linear and nonlinear control systems. If the system is linear and autonomous and satisfies the classical normality assumption, we improve the well known result on theExpand
Non-Lipschitz points and the SBV regularity of the minimum time function
This paper is devoted to the study of the Hausdorff dimension of the singular set of the minimum time function $T$ under controllability conditions which do not imply the Lipschitz continuity of $T$.Expand