Background Material on Asymptotic Analysis of Extremal Problems

Abstract

This chapter is intended to provide various facts, notions, and concepts which play a fundamental role in modern asymptotic analysis of optimization problems. We recall some main concepts and basic results of measure theory, Sobolev spaces, and boundary value problems which are used later. We include proofs only if the line of arguments is of importance for the understanding of subsequent remarks. For a deeper insight in the subject, we refer to the books of Adams (1975), Bucur and Buttazzo (2005), Evans and Gariepy (1992), Kantorovich and Akilov (1976), Lions and Magenes (1972), Maz’ya (1986), Yosida (1965), Ziemer (1989), and so on.