Moreau-Yosida Regularization of Degenerate State-Dependent Sweeping Processes

TL;DR

This paper introduces a new approach to degenerate state-dependent sweeping processes with irregular moving sets, using Moreau-Yosida regularization to establish solution existence under certain conditions.

Contribution

It extends the theory of sweeping processes by handling nonregular, subsmooth, and positively alpha-far moving sets through regularization techniques.

Findings

Existence of solutions proved under Lipschitz conditions

Applicable to nonregular, subsmooth moving sets

Advances understanding of degenerate state-dependent 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.