Bounce law at the corners of convex billiards Original Research Article

Let C be a convex subset of View the MathML source. Given any elastic shock solution x(·) of the differential inclusion View the MathML source the bounce of the trajectory at a regular point of the boundary of C follows the Descartes law. The aim of the paper is to exhibit the bounce law at the corners of the boundary. For that purpose, we define a sequence (Cε) of regular sets tending to C as ε→0, then we consider the approximate differential inclusion View the MathML source, and finally we pass to the limit when ε→0. For approximate sets defined by View the MathML source (where View the MathML source is the unit euclidean ball of View the MathML source), we recover the bounce law associated with the Moreau–Yosida regularization.