NONLINEAR DIFFERENTIAL VARIATIONAL INEQUALITIES WITH NONCONVEX SETS IN L-p SPACES

摘要

In this paper, we use recent results on proximal analysis in Banach spaces [7,9] to prove the existence of solutions of a particular form of nonconvex differential variational inequalities (NDVI) in L-P([0, 1], R) spaces with p >= 2. The proposed (NDVI) coincides with the well known nonconvex sweeping process when p = 2. Also, the convex sweeping process studied in Banach spaces in [6] is covered by our (NDVI) when the moving set is convex. Examples of nonconvex moving sets in L-p([0, 1], R) are stated. We also notice that the Lipschitz assumption on the moving set is weaker and easy to check relatively to the one used in [6].