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Journal of Convex Analysis 28 (2021), No. 2, 629--654
Copyright Heldermann Verlag 2021

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

Josť-Luis Menaldi
Dept. of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.

Carlos N. Rautenberg
Dept. of Mathematical Sciences, Center for Mathematics and Artificial Intelligence, George Mason University, Fairfax, VA 22030, U.S.A.

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.

Keywords: Mosco convergence, variational inequalities, quasi-variational inequalities.

MSC: 35J86, 35J60, 35R35, 65K10, 93E20.

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