Mathematical theory of hemivariational inequalities and applications

Title page
Preface
Introduction
Guidelines for the Reader, Abbreviations
1 Introductory Material
1.1 Elements of Convex Analysis
1.2 Elements of Nonconvex Nonsmooth Analysis
1.3 Maximal Monotone Operators and Variational Inequalities
1.4 On the Formulation of Hemivariational Inequalities and Related Topics
2 Pseudo-Monotonicity and Generalized Pseudo-Monotonicity
2.1 Pseudo-Monotone and Generalized Pseudo-Monotone Mappings. Basic Properties
2.2 Nonconvex Functions with Generalized Gradient of Pseudo- or Generalized Pseudo-Monotone Type
3 Hemivariational Inequalities for Static One-dimensional Nonconvex Superpotential Laws
3.1 Coercive Hemivariational Inequalities
3.2 Semicoercive Hemivariational Inequalities
3.3 The Substationarity of the Energy
3.4 Variational-Hemivariational Inequalities
3.5 Applications in Mechanics and Engineering
3.5.1 Contact of a Linear Elastic Body with an Adhesive Support
3.5.2 Adhesively Connected Sandwich Plates
4 Hemivariational Inequalities for Locally Lipschitz Functionals
4.1 The Class of Locally Lipschitz Functions with Pseudo-Monotone and Quasi-Pseudo-Monotone Generalized Gradients
4.2 Pointwise Minima and Maxima of Functions from the Classes QPM(V) and PM(V) and Compositions with Linear Compact Operators
4.3 Hemivariational Inequalities Involving Functions from QPM- and PM-Classes
4.4 Variational- Hemivariational Inequalities
4.5 Quasi-Hemivariational Inequalities
4.6 Applications to Mechanics and Engineering
4.6.1 Two- and Three-dimensional Nonconvex Superpotential Laws
4.6.2 The General Adhesive Contact and Friction Problem
4.6.3 On the Fuzzy Friction and Adhesive Contact Problem. The Case of Locking Support
4.6.4 Nonmonotone Multivalued Relations in Structural Analysis
4.6.5 Variational-Hemivariational Inequalities in the Theory of Laminated von Karman Plates
4.6.6 Rigid Viscoplastic Flow Problems in Cylindrical Pipes with Adhesion or Nonmonotone Friction
5 Hemivariational Inequalities for Multidimensional Superpotential Law
5.1 Formulation of the Problem
5.2 Hemivariational Inequalities with a Coercive Operator
5.3 Hemivariational Inequalities with Strongly Monotone Operator
5.4 Hemivariational Inequalities with Relaxed Directional Growth Condition
5.5 Applications to Mechanics, Engineering and Economics
5.5.1 Nonmonotone Skin Friction in Plane Elasticity
5.5.2 The General Problem of Masonry Structures
5.5.3 On the Nonconvex Semipermeability Problem
5.5.4 Hemivariational Inequalities in Nonlinear Elasticity Problems
5.5.5 Nonmonotone Laws in Networks
6 Noncoercive Hemivariational Inequalities Related to Free Boundary Problems
6.1 A System of a Variational and a Hemivariational Inequality Related to Delamination Problems
6.2 The Strain Energy Function
6.3 Study of the Case of Partial Delamination
6.4 Study of the General Case
7 Constrained Problems for Nonconvex Star-Shaped Admissible Sets
7.1 Distance Function for Star-Shaped Sets. Basic Properties
7.2 Constrained Hemivariational Inequalities
7.2.1 General Method
7.2.2 Union of a Finite Collection of Convex Sets
7.2.3 The Case of a Compact Operator
7.3 Constrained Problems with Strongly Monotone Operators
7.4 Variational Inequalities with Nonconvex Domain
7.5 Applications to the Plasticity Theory with Nonconvex Yield Condition
7.6 Applications to the Theory of Elasticity
7.6.1 The Signorini Problem in Nonlinear Elasticity for Star-Shaped Closed Sets
7.6.2 Constrained Skin Effects in Plane Nonlinear Elasticity
References
Index