H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 65 Citations 40,107 93 World Ranking 186 National Ranking 103

Research.com Recognitions

Awards & Achievements

2015 - Abel Prize For striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.

2014 - Steele Prize for Seminal Contribution to Research

2013 - Fellow of the American Mathematical Society

2011 - Fellow of the Royal Society of Canada Academy of Science

1995 - US President's National Medal of Science "For his fundamental contributions to linear and nonlinear partial differential equations, and applications, particularly in geometry and complex analysis, thus having a decisive impact on the development of mathematics and its applications over a period of years.", Awarded by President Clinton at a White House ceremony on October 18, 1995.

1994 - Steele Prize for Lifetime Achievement

1975 - Fellow of John Simon Guggenheim Memorial Foundation

1969 - Member of the National Academy of Sciences

1966 - Fellow of John Simon Guggenheim Memorial Foundation

1958 - Fellow of Alfred P. Sloan Foundation

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Partial differential equation
  • Geometry

His primary areas of study are Mathematical analysis, Dirichlet problem, Boundary value problem, Elliptic partial differential equation and Dirichlet boundary condition. In his research, Louis Nirenberg performs multidisciplinary study on Mathematical analysis and Symmetry. His study ties his expertise on Numerical partial differential equations together with the subject of Elliptic partial differential equation.

His work investigates the relationship between Numerical partial differential equations and topics such as Constant coefficients that intersect with problems in Pure mathematics. His study looks at the intersection of Elliptic curve and topics like Existence theorem with Mathematical physics. His biological study spans a wide range of topics, including Space and Plane.

His most cited work include:

  • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I (3354 citations)
  • Symmetry and related properties via the maximum principle (2334 citations)
  • Positive solutions of nonlinear elliptic equations involving critical sobolev exponents (2152 citations)

What are the main themes of his work throughout his whole career to date?

Louis Nirenberg spends much of his time researching Mathematical analysis, Pure mathematics, Elliptic partial differential equation, Parabolic partial differential equation and Boundary. His study in Boundary value problem, Quarter period, Semi-elliptic operator, Dirichlet problem and Free boundary problem falls within the category of Mathematical analysis. His Free boundary problem research is multidisciplinary, incorporating elements of Neumann boundary condition and Mixed boundary condition.

His Pure mathematics research is multidisciplinary, relying on both Discrete mathematics and Degree. Within one scientific family, Louis Nirenberg focuses on topics pertaining to First-order partial differential equation under Elliptic partial differential equation, and may sometimes address concerns connected to Linear differential equation. Louis Nirenberg focuses mostly in the field of Parabolic partial differential equation, narrowing it down to matters related to Existence theorem and, in some cases, Elliptic curve.

He most often published in these fields:

  • Mathematical analysis (58.06%)
  • Pure mathematics (23.39%)
  • Elliptic partial differential equation (19.35%)

What were the highlights of his more recent work (between 2000-2016)?

  • Mathematical analysis (58.06%)
  • Pure mathematics (23.39%)
  • Hopf lemma (5.65%)

In recent papers he was focusing on the following fields of study:

Louis Nirenberg mostly deals with Mathematical analysis, Pure mathematics, Hopf lemma, Boundary and Discrete mathematics. He performs integrative study on Mathematical analysis and Viscosity in his works. The study incorporates disciplines such as Differential and Regular polygon in addition to Pure mathematics.

His research investigates the connection between Boundary and topics such as Mean curvature that intersect with problems in Constant. His work carried out in the field of Discrete mathematics brings together such families of science as Topological entropy in physics and Topological quantum number. His research integrates issues of Elliptic curve point multiplication and Singular solution in his study of Elliptic partial differential equation.

Between 2000 and 2016, his most popular works were:

  • Topics in Nonlinear Functional Analysis (790 citations)
  • Properties of Solutions of Ordinary Differential Equations in Banach Space (290 citations)
  • Estimates for elliptic systems from composite material (230 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Partial differential equation
  • Geometry

His primary areas of study are Mathematical analysis, Pure mathematics, Viscosity, Boundary and Finsler manifold. Louis Nirenberg integrates Mathematical analysis with Perturbation theory in his research. His study in the field of Complex manifold, Spectral theorem and Several complex variables also crosses realms of Artin approximation theorem and Complex analysis.

Louis Nirenberg interconnects Metric and Combinatorics in the investigation of issues within Boundary. Louis Nirenberg has included themes like Supersingular elliptic curve, Quarter period, Elliptic rational functions, Gravitational singularity and Jacobi elliptic functions in his Elliptic partial differential equation study. His work deals with themes such as Elliptic curve point multiplication and Schoof's algorithm, which intersect with Singular solution.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Top Publications

Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I

S. Agmon;A. Douglis;L. Nirenberg.
Communications on Pure and Applied Mathematics (1959)

5881 Citations

Positive solutions of nonlinear elliptic equations involving critical sobolev exponents

Haïm Brezis;Louis Nirenberg.
Communications on Pure and Applied Mathematics (1983)

3314 Citations

Symmetry and related properties via the maximum principle

B. Gidas;Wei Ming Ni;L. Nirenberg.
Communications in Mathematical Physics (1979)

3149 Citations

On functions of bounded mean oscillation

F. John;L. Nirenberg.
Communications on Pure and Applied Mathematics (1961)

2008 Citations

On elliptic partial differential equations

L. Nirenberg.
Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze (1959)

1950 Citations

Partial regularity of suitable weak solutions of the navier‐stokes equations

L. Caffarelli;R. Kohn;L. Nirenberg.
Communications on Pure and Applied Mathematics (1982)

1515 Citations

Topics in Nonlinear Functional Analysis

Louis Nirenberg.
(2001)

1229 Citations

First order interpolation inequalities with weights

L. Caffarelli;R. Kohn;L. Nirenberg.
Compositio Mathematica (1984)

1060 Citations

Complex Analytic Coordinates in Almost Complex Manifolds

A. Newlander;L. Nirenberg.
Annals of Mathematics (1957)

1025 Citations

The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian

L. Caffarelli;L. Nirenberg;J. Spruck.
Acta Mathematica (1985)

805 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

If you think any of the details on this page are incorrect, let us know.

Contact us

Top Scientists Citing Louis Nirenberg

YanYan Li

YanYan Li

Rutgers, The State University of New Jersey

Publications: 106

Haim Brezis

Haim Brezis

Rutgers, The State University of New Jersey

Publications: 77

Jean Dolbeault

Jean Dolbeault

Paris Dauphine University

Publications: 77

Juncheng Wei

Juncheng Wei

University of British Columbia

Publications: 76

François Hamel

François Hamel

Aix-Marseille University

Publications: 72

Vladimir Maz'ya

Vladimir Maz'ya

Linköping University

Publications: 61

Henri Berestycki

Henri Berestycki

Centre d'Analyse et de Mathématique Sociales

Publications: 55

Dachun Yang

Dachun Yang

Beijing Normal University

Publications: 53

Enrico Valdinoci

Enrico Valdinoci

University of Western Australia

Publications: 52

Zhi-Qiang Wang

Zhi-Qiang Wang

Utah State University

Publications: 51

Marco Squassina

Marco Squassina

Catholic University of the Sacred Heart

Publications: 49

Neil S. Trudinger

Neil S. Trudinger

Australian National University

Publications: 47

Monica Musso

Monica Musso

University of Bath

Publications: 46

Nassif Ghoussoub

Nassif Ghoussoub

University of British Columbia

Publications: 46

Maria J. Esteban

Maria J. Esteban

Paris Dauphine University

Publications: 45

Something went wrong. Please try again later.