Bounce problem with weak hypotheses of regularity (Q1822038)

The elastic bounce problem is formulated under very general hypotheses. More precisely we consider the motion of a material point constrained to move in a domain \(\Omega \subset {\mathbb{R}}^ n\), bouncing against its boundary, and we suppose that \(\Omega\) is neither regular nor convex. Assuming that \(\Omega\) is in the class of p-convex sets and \(\partial \Omega \in C^{0,1}\), an existence theorem is stated.