On Some Quasi-Variational Inequalities and Other Problems with Moving Sets

TL;DR

This paper investigates the implications of Mosco convergence on problems involving moving sets, highlighting its impact on quasi-variational inequalities, finite element methods, and impulse control, with historical and modern perspectives.

Contribution

It explores the effects of Mosco convergence on applied problems with moving sets, connecting it to various mathematical and computational methods.

Findings

Mosco convergence influences the density of convex intersections

It affects finite element approximation techniques

Implications for quasi-variational inequalities and impulse problems

Abstract

Since its introduction over 50 years ago, the concept of Mosco convergence has permeated through diverse areas of mathematics and applied sciences. These include applied analysis, the theory of partial differential equations, numerical analysis, and infinite dimensional constrained optimization, among others. In this paper we explore some of the consequences of Mosco convergence on applied problems that involve moving sets, with some historical accounts, and modern trends and features. In particular, we focus on connections with density of convex intersections, finite element approximations, quasi-variational inequalities, and impulse problems.