Fritz John | Academic Influence

Fritz John's AcademicInfluence.com Rankings

Fritz John

Mathematics

#204

World Rank

#460

Historical Rank

#97

USA Rank

Applied Mathematics

#13

World Rank

#14

Historical Rank

#9

USA Rank

Measure Theory

#215

World Rank

#334

Historical Rank

#95

USA Rank

mathematics Degrees

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Mathematics

Fritz John's Degrees

PhD Mathematics University of Göttingen

Why Is Fritz John Influential?

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According to Wikipedia, Fritz John was a German-born mathematician specialising in partial differential equations and ill-posed problems. His early work was on the Radon transform and he is remembered for John's equation. He was a 1984 MacArthur Fellow.

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Fritz John's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Partial differential equations (1967) (1165)
On functions of bounded mean oscillation (1961) (1034)
Plane Waves and Spherical Means: Applied To Partial Differential Equations (1981) (571)
Blow-up of solutions of nonlinear wave equations in three space dimensions (1979) (501)
On the motion of floating bodies. I (1949) (457)
Formation of singularities in one‐dimensional nonlinear wave propagation (1974) (368)
On the motion of floating bodies II. Simple harmonic motions (1950) (354)
Rotation and strain (1961) (344)
Continuous dependence on data for solutions of partial differential equations with a prescribed bound (1960) (306)
Introduction to Calculus and Analysis (1991) (294)
Blow-Up for Quasi-Linear Wave Equations in Three Space Dimensions (1981) (249)
Plane strain problems for a perfectly elastic material of harmonic type (1960) (242)
Nonlinear wave equations, formation of singularities (1990) (209)
Almost global existence to nonlinear wave equations in three space dimensions (1984) (199)
The ultrahyperbolic differential equation with four independent variables (1938) (167)
Estimates for the derivatives of the stresses in a thin shell and interior shell equations (1965) (150)
The Dirichlet Problem for a Hyperbolic Equation (1941) (122)
Trends and perspectives in applied mathematics (1994) (114)
On integration of parabolic equations by difference methods: I. Linear and quasi‐linear equations for the infinite interval (1952) (92)
On quasi‐isometric mappings, II (1968) (92)
Quasi-Isometric Mappings (1985) (91)
Formation of singularities in elastic waves (1984) (78)
On linear partial differential equations with analytic coefficients unique continuation of data (1949) (76)
Plane elastic waves of finite amplitude. Hadamard materials and harmonic materials (1966) (73)
The fundamental solution of linear elliptic differential equations with analytic coefficients (1950) (68)
Almost global existence of elastic waves of finite amplitude arising from small initial disturbances (1988) (67)
Uniqueness of non‐linear elastic equilibrium for prescribed boundary displacements and sufficiently small strains (1972) (66)
Contributions to the Theory of Partial Differential Equations. (1955) (60)
Refined interior equations for thin elastic shells (1971) (56)
Numerical solution of the equation of heat conduction for preceding times (1955) (54)
Lectures on advanced numerical analysis (1967) (54)
Lower bounds for the life-span of solutions of nonlinear wave equations in three dimensions. (1982) (51)
Delayed singularity formation in solution of nonlinear wave equations in higher dimensions (1976) (50)
Bestimmung einer Funktion aus ihren Integralen Über gewisse Mannigfaltigkeiten (1934) (50)
Existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data (1987) (49)
Two-dimensional potential flows with a free boundary† (1953) (42)
Introduction to Calculus and Analysis Volume II/1 (2000) (38)
Polar correspondence with respect to a convex region (1937) (37)
Linear Partial Differential Equations with Analytic Coefficients. (1943) (37)
A note on “improper” problems in partial differential equations (1955) (36)
Abhängigkeiten zwischen den Flächenintegralen einer stetigen Funktion (1935) (35)
Finite amplitude waves in a homogeneous isotropic elastic solid (1977) (35)
Advanced numerical analysis (1956) (26)
On Integration of Parabolic Equations By Difference Methods (1985) (23)
Special solutions of certain difference equations (1939) (20)
Derivatives of continuous weak solutions of linear elliptic equations (1953) (17)
Refined Interior Shell Equations (1969) (17)
Continuation and reflection of solutions of partial differential equations (1957) (16)
General Properties of Solutions of Linear Elliptic Partial Differential Equations (1985) (14)
A criterion for univalency brought up to date (1976) (14)
Solutions of Second Order Hyperbolic Differential Equations with Constant Coefficients in a Domain with a Plane Boundary (1954) (12)
Non-admissible data for differential equations with constant coefficients† (1957) (11)
Delayed singularity formation for solutions of nonlinear partial differential equations in higher dimensions. (1976) (10)
Addendum to: Algebraic conditions for hyperbolicity of systems of partial differential equations (1978) (10)
Taylor’s Expansion (1999) (10)
A priori estimates, geometric effects and asymptotic behavior (1975) (8)
Remark on [2] (1985) (8)
A note on my paper: “On symmetric matrices whose eigenvalues satisfy linear inequalities” (1966) (7)
Remark on Harmuth's "Corrections of Maxwell's Equations for Signals I" (1991) (7)
Long time effects of nonlinearity in second order hyperbolic equations (1986) (6)
Restrictions on the coefficients of hyperbolic systems of partial differential equations. (1977) (6)
A note on the maximum principle for elliptic differential equations (1938) (5)
On harmonic vibrations out of phase with the exciting force (1948) (5)
FUNCTIONS WHOSE GRADIENT IS BOUNDED BY THE RECIPROCAL DISTANCE FROM THE BOUNDARY OF THEIR DOMAIN (1974) (5)
Differential equations with approximate and improper date (1955) (5)
Solutions of quasi-linear wave equations with small initial data (1989) (5)
Instability of Finite Amplitude Elastic Waves (1981) (5)
Appendix to the preceding paper of W. T. Koiter (1969) (4)
The Single First Order Equation (1978) (4)
Identitäten zwischen dem Integral einer willkürlichen Funktion und unendlichen Reihen (1935) (3)
THE ACTION OF FLOATING BODIES ON OCEAN WAVES (1949) (3)
Distance Changes in Deformations with Small Strain (1985) (3)
Moments of inertia of convex regions (1936) (3)
The Cauchy Problem for Higher Order Equations (1975) (3)
Über die Vollständigkeit der Relationen von Morse für die Anzahlen kritischer Punkte (1934) (3)
Discontinuous convex solutions of difference equations (1941) (2)
Numerical Solution of Problems which are not Well Posed in the Sense of Hadamardd (1985) (2)
The Transition from Thin Plate to Membrane in the Case of a Plate under Uniform Tension (1985) (2)
Special topics in partial differential equations (1953) (1)
Functions of Several Variables and their Derivatives (1989) (1)
Second Order Linear Equations with Constant Coefficients (1975) (1)
Partial differential equations, 1952-1953 (1953) (1)
Note on the paper “On Quasi-Isometric Mappings, I” (1985) (1)
The Fundamental Solution of a Linear Elliptic Differential Equation with Analytic Coefficients (1981) (1)
The Initial Value Problem for Hyperbolic Homogeneous Equations with Constant Coefficients (1981) (1)
Perfectly Elastic Bodies of Harmonic Type (1985) (1)
Research in Continuum Mechanics. (1981) (1)
Ordinary differential equations : 1964-1965 (1965) (1)
Note on the paper “on quasi-isometric mappings, I”. C.P.A.M., vol. XXI, 1968, pp. 77-110 (1972) (1)
Non-Existence of Global Solutions of partial of F(u sub t) with Respect to t in Two and Three Space Dimensions. (1984) (1)
Nonexistence of global solutions of □u = F(utt) and of □v = F′(vt)vtt in three space dimensions (1980) (1)
Uniqueness for nonlinear wave equations (1990) (1)
A Walk Through Partial Differential Equations (1984) (1)
Longtime existence for solutions of nonlinear wave equations with small initial data (1990) (0)
On behavior of solutions of partial differential equations (1953) (0)
Identities for Spherical Means (1981) (0)
Equations in one space variable (1990) (0)
The transition from thin plate to membrane in the equations of V. Karman — Föppl (1985) (0)
Erratum to: Delayed Singularity Formation in Solutions of Nonlinear Wave Equations in Higher Dimensions (1985) (0)
American Mathematical Society Edited by with the Cooperation of Index to Volume 15 [december Cohomology of Groups in Arbitrary Categories (0)
Review: Dorothy L. Bernstein, Existence theorems in partial differential equations (1951) (0)
Derivatives of Solutions of Linear Elliptic Partial Differential Equations (1985) (0)
Differentiability Properties of Solutions of Elliptic Systems (1981) (0)
Second-order equations: hyperbolic equations for functions of two independent variables (1978) (0)
H. Lewey’s Example of a Linear Equation without Solutions (1982) (0)
Error estimates in the derivation of the non-linear equations for elastic plates (1963) (0)
Higher-order elliptic equations with constant coefficients (1978) (0)
Differential Equations for the Simplest Types of Vibration (1989) (0)
Characteristic manifolds and the Cauchy problem (1978) (0)
Hyperbolic equations in higher dimensions (1978) (0)
Partial differential equations. 1952-53/ Fritz John (1953) (0)
Partial Differential Equations: Applied Mathematical Sciences, Volume I. (1972) (0)
Blow-Up of Radial Solutions of Linear Wave Equation U = Partial Derivative F of U Sub t with Respect to the Partial Derivative of T in Three Space Dimensions. (1983) (0)
Erratum to: Blow-Up of Solutions of Nonlinear Wave Equations in Three Space Dimensions (1985) (0)
Vectors, Matrices, Linear Transformations (2000) (0)
A Representation of Stieltjes Integrals by Conditionally Convergent Series (1937) (0)
Mensch und Scholle. Von P. Krische. Kartenwerk zur Geschichte und Geographie des Kulturbodens. Bd. II (Bd. 4 der Gesamtreihe). 206 S., 361 Karten von 35 Ländern. 2°. Deutsche Verlagsges., Berlin 1939. Pr. kart. RM. 27,50. (1941) (0)
Determination of a Function from Its Integrals over Spheres of a Fixed Radius (1981) (0)
Developments and Applications of the Differential Calculus (1989) (0)
Nonexistence of global solutions of squareu = F(u) and of squarev = F'(v)v in three space dimensions. (1980) (0)
The Fundamental Ideas of the Integral and Differential Calculus (1999) (0)
Regularity Properties for Integrals of Solutions over Time-like Lines (1981) (0)
Nonexistence of global solutions of iu = F ( Utt ) and of Dv = F ' ( Vt ) vtt in three space dimensions ( asymptotic behavior of solutions / nonlinear equations and systems / wave equation ) (0)
The Initial Value Problem for Maxwell’s Equations for Two Media Separated by a Plane: Dedicated to Hans Rademacher on the occasion of his seventieth birthday (1985) (0)
The Techniques of Calculus (1999) (0)
Applications in Physics and Geometry (1999) (0)
Infinite Sums and Products (1989) (0)
Decomposition of an Arbitrary Function into Plane Waves (1981) (0)
The Theorems of Asgeirsson and Howard (1981) (0)
The Role of Inequalities in the Mathematical Theory of Elasticity (1966) (0)
Review: Robert Sauer, Anfangswertprobleme bei partiellen Differentialgleichungen (1961) (0)
Existence for large times of finite amplitude elastic waves arising from small disturbances. (1988) (0)
Relations Between Surface and Volume Integrals (1989) (0)
II. Pyodermien, Diphtherie, Milzbrand (1936) (0)
The Cauchy Problem for Linear Hyperbolic Equations in General (1975) (0)
The initial value problem for Maxwell's equations for two media separated by a plane (1962) (0)

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