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On the solution set of the nonconvex sweeping process

Andrea Gavioli — 1999

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We prove that the solutions of a sweeping process make up an R δ -set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.

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