The book "Inequality Problems in Mechanics and Applications" by P. D. Panagiotopoulos, published by Birkhäuser in 1985, is a comprehensive treatise on the mathematical and mechanical aspects of inequality problems. The author, P. D. Panagiotopoulos, is affiliated with the Aristotle University of Thessaloniki and RWTH Aachen University. The book is divided into three main parts: Introductory Topics, Inequality Problems, and Numerical Applications. **Introductory Topics (Chapters 1 and 2)**: - **Chapter 1**: Introduces essential notions and propositions of functional analysis, including topological vector spaces, duality, function spaces, and Sobolev spaces. - **Chapter 2**: Covers elements of convex analysis, such as convex sets and functionals, minimization of convex functionals, subdifferentiability, subdifferential calculus, and maximal monotone operators. **Inequality Problems (Chapters 3 to 9)**: - **Chapters 3-4**: Focus on convex and nonconvex superpotentials in various areas of nonrelativistic mechanics, emphasizing the connection to multivalued differential or integral equations, minimization theory, and substationarity theory. - **Chapters 5-9**: Deal with unilateral boundary value problems (BVPs) in mechanics, including friction problems, subdifferential boundary conditions, von Kármán plates, thermoelasticity, plasticity, and viscoplasticity. Each chapter provides a detailed study of specific types of inequality problems and their solutions. **Numerical Applications (Chapters 10 and 11)**: - **Chapter 10**: Discusses the numerical treatment of static inequality problems, including unilateral contact and friction problems, and linear analysis approaches. - **Chapter 11**: Explores incremental and dynamic inequality problems, such as elastoplastic analysis and dynamic unilateral contact problems. The book aims to bridge the gap between mathematical theory and practical applications, making it accessible to both mathematicians and engineers. It is structured to be self-contained, with detailed guidelines for readers of varying backgrounds. The author acknowledges the contributions of several key figures in the field, including G. Fichera, J. L. Lions, G. Maier, and J. J. Moreau, and provides a comprehensive list of references and appendices for further study.The book "Inequality Problems in Mechanics and Applications" by P. D. Panagiotopoulos, published by Birkhäuser in 1985, is a comprehensive treatise on the mathematical and mechanical aspects of inequality problems. The author, P. D. Panagiotopoulos, is affiliated with the Aristotle University of Thessaloniki and RWTH Aachen University. The book is divided into three main parts: Introductory Topics, Inequality Problems, and Numerical Applications. **Introductory Topics (Chapters 1 and 2)**: - **Chapter 1**: Introduces essential notions and propositions of functional analysis, including topological vector spaces, duality, function spaces, and Sobolev spaces. - **Chapter 2**: Covers elements of convex analysis, such as convex sets and functionals, minimization of convex functionals, subdifferentiability, subdifferential calculus, and maximal monotone operators. **Inequality Problems (Chapters 3 to 9)**: - **Chapters 3-4**: Focus on convex and nonconvex superpotentials in various areas of nonrelativistic mechanics, emphasizing the connection to multivalued differential or integral equations, minimization theory, and substationarity theory. - **Chapters 5-9**: Deal with unilateral boundary value problems (BVPs) in mechanics, including friction problems, subdifferential boundary conditions, von Kármán plates, thermoelasticity, plasticity, and viscoplasticity. Each chapter provides a detailed study of specific types of inequality problems and their solutions. **Numerical Applications (Chapters 10 and 11)**: - **Chapter 10**: Discusses the numerical treatment of static inequality problems, including unilateral contact and friction problems, and linear analysis approaches. - **Chapter 11**: Explores incremental and dynamic inequality problems, such as elastoplastic analysis and dynamic unilateral contact problems. The book aims to bridge the gap between mathematical theory and practical applications, making it accessible to both mathematicians and engineers. It is structured to be self-contained, with detailed guidelines for readers of varying backgrounds. The author acknowledges the contributions of several key figures in the field, including G. Fichera, J. L. Lions, G. Maier, and J. J. Moreau, and provides a comprehensive list of references and appendices for further study.