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.

Author information

Contact details are reproduced from the original publication and may be historical.

José-Luis Menaldi

Dept. of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.

menaldi@wayne.edu

Carlos N. Rautenberg

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

crautenb@gmu.edu

Keywords

  • Mosco convergence
  • variational inequalities
  • quasi-variational inequalities

Mathematics Subject Classification

35J86, 35J60, 35R35, 65K10, 93E20

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Suggested citation

J.-L. Menaldi, C. N. Rautenberg. “On Some Quasi-Variational Inequalities and Other Problems with Moving Sets.” Journal of Convex Analysis 28 (2021), No. 2, 629–654. https://doi.org/10.68381/jca28036

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