Enrico Magenes Livres

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.

Lectures: B. Malgrange: Operatori differenziali.- J. Mikusinski: Une introduction élémentaire à la théorie des distributions de plusieurs variables.- L. Schwartz: I. Trasformata di Fourier delle distribuzioni; II. Spazi di Hilbert e nuclei associati.- Seminars: J. B. Diaz: Solutions of the singular Cauchy problem for a singular system of partial differential equations in the mathematical theory of dynamical elasticity.- J. Gobert: Un cas critique du problème de Dirichlet-Neumann.- J. L. Lions: Espaces d´interpolation. Espaces de moyenne.- J. Sebastiao e Silva: Sur l´axiomatique des distributions et ses possibles modèles.- S. Zaidman: Distribuzioni quasi-periodiche e applicazioni.