Fritz John

The mathematical works of Fritz John whose deep and original ideas have had a great influence on the development of various fields in mathema tical analysis are made available with these volumes. His works are certainly well known to the experts, but knowledge of his contributions may not have spread as widely as it should have. For example, the concept of functions of bounded mean oscillations plays a central role in harmonic analysis today, but it is perhaps less known that this class of functions was introduced by John as early as 1961, motivated by his work in elasticity theory. With the publication of this collection, a wider circle of mathematicians will become familiar with, and appreciate, the fertile ideas of Fritz John. The organization of these two volumes was undertaken in consultation with the author. It was decided not to present the papers in chronological order, but rather to subdivide them into ten sections representing different mathematical topics to which John has contributed. Commentaries made by experts in the fields are appended to each section. Since the division into sec tions could, of course, not be made sharply, there are several overlaps. For instance, the comments of Louis Nirenberg refer to Elasticity Theory VI, Geometric Inequalities VIII, and Functions of Bounded Mean Oscillations IX. To help the reader, cross-references and remarks by the author will be found at the end of each section.

Contenu

• Volume 1.- Preface.- Foreword.- Publications of Fritz John.- Biographical Sketch.- Acknowledgements.- I Papers on Random Transfer.- [2] Bestimmung einer Funktion aus ihren Integralen über gewisse Mannigfaltigkeiten (1934).- [4] Abhängigkeiten zwischen den Flächenintegralen einer stetigen Funktion (1935).- [8] The ultrahyperbolic differential equation with four independent variables (1938).- Remarks on [2].- Commentary on [2], [4], and [8].- II Papers on Differential Equations.- [9] A note on the maximum principle for elliptic differential equations (1938).- [16] Linear partial differential equations with analytic coefficients (1943).- [23] On linear partial differential equations with analytic coefficients (unique continuation of data) (1949).- [25] The fundamental solution of linear elliptic differential equations with analytic coefficients (1950).- [27] General properties of solutions of linear elliptic partial differential equations (1951).- [31] Derivatives of continuous weak solutions of linear elliptic equations (1953).- [33] Solutions of second order hyperbolic differential equations with constant coefficients in a domain with a plane boundary (1954).- [51] The initial value problem for Maxwell's equations for two media separated by a plane (1962).- [89] Algebraic conditions for hyperbolicity of systems of partial differential equations (1978).- [90] Addendum to: Algebraic conditions for hyperbolicity of systems of partial differential equations (1978).- Commentary on [16], [23], and [41].- Commentary on [25].- Commentary on [36].- Commentary on [42].- Commentary on [89].- III Papers on Ill-posed Problems.- [14] The Dirichlet problem for a hyperbolic equation (1941).- [38] A note on improper problems in partial differential equations (1955).- [39]Numerical solution of the equation of heat conduction for preceding times (1955).- [41] Non-admissible data for differential equations with constant coefficients (1957).- [45] Numerical solution of problems which are not well posed in the sense of Hadamard (1959).- [47] Continuous dependence on data for solutions of partial differential equations with a prescribed bound (1960).- Commentary on [38] and [47].- Commentary on [39] and [47].- IV Papers on Formation of Singularities.- [77] Formation of singularities in one-dimensional nonlinear wave propagation (1974).- [85] Delayed singularity formation in solutions of nonlinear wave equations in higher dimensions (1976).- [92] Blow-up of solutions of nonlinear wave equations in three space dimensions (1979) :.- [94] Blow-up quasi-linear wave equations in three space dimensions (1981).- [98] Lower bounds for the life span of solutions of nonlinear wave equations in three dimensions (1983).- [98] Lower bounds for the life span of solutions of nonlinear wave equations in three dimensions (1983).- [101] Formation of singularities in elastic waves (1984).- Corrections to [85] and [92].- Commentary on [77], [85], [92], and [94].- Collected Mathematical Papers ordered chronologically according to the date of original publication.