Jacques-Louis Lions Book order

The book explores the development of deterministic optimal control theory, focusing on key components such as admissible controls, system states derived from a specified operator model, and precise observations of these states. It emphasizes the relationship between control inputs and the resulting system behavior, culminating in the formulation of a cost function that quantifies economic outcomes. This structured approach offers a comprehensive framework for understanding and applying optimal control in various scenarios.

This volume delves into non-homogeneous boundary value problems for specific evolution equations, focusing on parabolic and hyperbolic operators. It explores regularity, transposition, and interpolation methods, highlighting new regularity results. The application of these findings to optimal control problems is a key feature, particularly concerning boundary conditions. Additionally, the book addresses the characterization of well-posed problems and hints at further applications, including numerical analysis, to be explored in the subsequent volume.

The book explores non-homogeneous boundary value problems involving linear differential operators within open subsets of R. It establishes a framework for seeking unique solutions that continuously depend on given function spaces. The focus is on determining families of function spaces and their associations, which are deemed "natural" for the problem at hand. The work emphasizes the flexibility in choosing function spaces and boundary conditions, making it a valuable resource for applications in mathematical analysis and differential equations.