Collected papers
Author(s)
Bibliographic Information
Collected papers
（Contemporary mathematicians）
Birkhäuser, 1985
- : set
- : set : Basel
- v. 1
- v. 1 : Basel
- v. 2
- v. 2 : Basel
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English and German
Description and Table of Contents
- Volume
-
: set ISBN 9780817632656
Description
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."
- Volume
-
v. 1 ISBN 9780817632663
Description
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.
Table of Contents
- Volume 1.- Preface.- Foreword.- Publications of Fritz John.- Biographical Sketch.- Acknowledgements.- I Papers on Random Transfer.- [2] Bestimmung einer Funktion aus ihren Integralen uber gewisse Mannigfaltigkeiten (1934).- [4] Abhangigkeiten zwischen den Flachenintegralen 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.
- Volume
-
v. 2 ISBN 9780817632670
Table of Contents
- Fritz John
- Collected Works Contents - Volume 2.- V Papers on Numerical Methods.- [29] On integration of parabolic equations by difference methods (1952).- Commentary on [29].- VI Papers on Elasticity Theory.- [46] Plane strain problems for a perfectly elastic material of harmonic type (1960).- [51a] Perfectly elastic bodies of harmonic type (1963).- [56] Estimates for the derivatives of the stresses in a thin shell and interior shell equations (1965).- [59] Plane elastic waves of finite amplitude (1966).- [70] Distance changes in deformations with small strain (1970).- [71] Refined interior equations for thin plastic shells (1971).- [74] The transition from thin plate to membrane in the case of a plate under uniform tension (1972).- [75] Uniqueness of nonlinear elastic equilibrium for prescribed boundary displacements and sufficiently small strains (1972).- [80] The transition from thin plate to membrane in the equations of V. Karman-Foeppl (1975).- [87] Finite amplitude waves in a homogeneous isotropic elastic solid (1977).- [96] Instability of finite amplitude elastic waves (1981).- Commentary on [56], [71], and [74].- VII Papers on Water Waves.- [18] Waves in the presence of an inclined barrier (1948).- [22] On the motion of floating bodies, I (1949).- [24] On the motion of floating bodies, II (1950).- [32] Two-dimensional potential flows with a free boundary (1953).- Commentary on [22], [24], and [32].- VIII Papers on Geometric Inequaities and Convexity.- [5] Moments of inertia of convex regions (1936).- [7] Polar correspondence with respect to a convex region (1937).- [10] Special solutions of certain difference equations (1939).- [11] An inequality for convex bodies (1940).- [12] Discontinuous convex solutions of difference equations (1941).- [17] Extremum problems with inequalities as subsidiary conditions (1948).- [60] On symmetric matrices whose eigenvalues satisfy linear inequalities (1966).- [65] A note on my paper, "On symmetric matrices whose eigenvalues satisfy linear inequalities" (1968).- [63] On quasi-isometric mappings, I (1968).- [63a] Note on the paper, "On quasi-isometric mappings, I" (1972).- [64] On quasi-isometric mappings, II (1969).- [73] Bounds for deformations in terms of average strains (1972).- [84] A criterion for univalencv brought up to date (1976).- Remarks on [17], [63], [64], and [84].- Commentary on [17].- IX Papers on Functions of Bounded Mean Oscillations.- [48] Rotation and strain (1961).- [49] (With L. Nirenberg) On Functions of bounded mean oscillation (1961).- [54] Quasi-isometric mappings (1964).- [78] Inunctions whose gradient is bounded by reciprocal distance from the boundary of their domain (1974).- Remark on [48].- Commentary on [48], [49], [54], [63], [64], [75], and [51a].- X Miscellaneous.- [1] UEber die Vollstandigkeit der Relationen von Morse fur die Anzahlen kritischer Punkte (1943).- [3] Identitaten zwischen dem Integral einer willktirluchen Funktion und unendlichen Reihen (1935).- [116] A representation of Stieltjes integrals by conditionally convergent series (1937).- [20] On harmonic vibrations out of phase with the exciting force (1948).- Collected Mathematical Papers ordered chronologically according to the date of original publication.
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