Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions

1. Introductory Topics.- 1. Essential Notions and Propositions of Functional Analysis.- 1.1 Topological Vector Spaces and Related Subjects.- 1.1.1 Topological Spaces and Continuous Mappings.- 1.1.2 Locally Convex Topological Vector Spaces, Normed Spaces and Linear Mappings.- 1.2 Duality in Topological Vector Spaces.- 1.2.1 Duality. Weak and Strong Topologies.- 1.2.2 Topologically Dual Pairs of Vector Spaces.- 1.2.3 Duality in Normed and Hilbert Spaces.- 1.2.4 Transpose of a Continuous Linear Mapping Scales of Hilbert Spaces. The Lax-Milgram Theorem.- 1.3 Certain Function Spaces and Their Properties.- 1.3.1 The Spaces $$ {C^m}\left( \Omega \right),{C^m}\left( {\overline \Omega } \right),D\left( \Omega…