Jacques-Louis Lions Livres

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.

S. Albertoni: Alcuni metodi di calcolo nella teoria della diffusione dei neutroni.- I. Babuska: Optimization and numerical stability in computations.- J. H. Bramble: Error estimates in elliptic boundary value problems.- G. Capriz: The numerical approach to hydrodynamic problems.- A. Dou: Energy inequalities in an elastic cylinder.- T. Doupont: On the existence of an iterative method for the solution of elliptic difference equation with an improved work estimate.- J. Douglas, J. R. Cannon: The approximation of harmonic and parabolic functions of half-spaces from interior data.- B. E. Hubbard: Error estimates in the fixed Membrane problem.- K. Jorgens: Calculation of the spectrum of a Schrödinger operator.- A. Lasota: Contingent equations and boundary value problems.- J. L. Lions: Réduction à des problèmes du type Cauchy-Kowalewska.- J. L. Lions: Problèmes aux limites non homogènes à données irrégulières; une méthode d’approximation.- J. L. Lions: Remarques sur l’approximation régularisée de problèmes aux limites.- W. V. Petryshyn: On the approximation-solvability of nonlinear functional equations in normed linear spaces.- P. A. Raviart: Approximation des équations d’évolution par des méthodes variationnelles.- M. Sibony, H. Brezis: Méthodes d’approximation et d’itération pour les operateurs monotones.- V. Thomee: Some topics in stability theory for partial difference operators.