Moreau-yosida regularization of degenerate state-dependent sweeping processes

Abstract

In this paper, we introduce and study degenerate state-dependent sweeping processes with nonregular moving sets (subsmooth and positively alpha-far). Based on the Moreau-Yosida regularization, we prove the existence of solutions under the Lipschitzianity of the moving sets with respect to the truncated Hausdorff distance.