@article{AGav99, AUTHOR = {Gavioli, Andrea}, TITLE = {On the solution set of the nonconvex sweeping process}, JOURNAL = {Discuss. Math. Differential Inclusions, Control and Optimization}, FJOURNAL = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization}, VOLUME = {19}, YEAR = {1999}, PAGES = {4565}, ISSN = {15099407}, ABSTRACT = {We prove that the solutions of a sweeping process make up an $R_{\d}$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.}, }
