H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 87 Citations 38,315 235 World Ranking 43 National Ranking 27

Research.com Recognitions

Awards & Achievements

2003 - Member of the National Academy of Sciences

1994 - Fellow of the American Academy of Arts and Sciences

1989 - Member of Academia Europaea

1988 - Academie des sciences, France

1985 - Ampère Prize (Prix Ampère de l’Électricité de France), French Academy of Sciences

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Quantum mechanics
  • Pure mathematics

Haim Brezis mostly deals with Mathematical analysis, Pure mathematics, Partial differential equation, Nonlinear system and Sobolev space. His work in Elliptic curve, Boundary value problem, Dirichlet problem, Nonlinear Schrödinger equation and Heat equation is related to Mathematical analysis. Haim Brezis combines subjects such as Modes of convergence, Calculus of variations, Nonlinear functional analysis and Class with his study of Pure mathematics.

His Nonlinear system research focuses on Mathematical physics and how it connects with Duality. His Sobolev space research integrates issues from Discrete mathematics, Finite difference, Bounded function and Space. His studies in Sobolev inequality integrate themes in fields like Interpolation space and Inequality.

His most cited work include:

  • Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert (2679 citations)
  • Functional Analysis, Sobolev Spaces and Partial Differential Equations (2479 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?

His scientific interests lie mostly in Mathematical analysis, Pure mathematics, Combinatorics, Sobolev space and Nonlinear system. His study in Partial differential equation, Boundary value problem, Elliptic curve, Measure and Gravitational singularity is carried out as part of his Mathematical analysis studies. His Partial differential equation study combines topics in areas such as Mathematical physics, Existence theorem and Differential equation.

His Pure mathematics study incorporates themes from Discrete mathematics and Norm. The Combinatorics study combines topics in areas such as Nabla symbol, Omega, Domain, Bounded function and Function. His study in Sobolev space is interdisciplinary in nature, drawing from both Space, Homotopy, Topology and Degree.

He most often published in these fields:

  • Mathematical analysis (47.06%)
  • Pure mathematics (31.58%)
  • Combinatorics (32.82%)

What were the highlights of his more recent work (between 2015-2021)?

  • Sobolev space (28.79%)
  • Combinatorics (32.82%)
  • Omega (20.74%)

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

Sobolev space, Combinatorics, Omega, Non local and Pure mathematics are his primary areas of study. His research in Sobolev space intersects with topics in Interpolation inequality, Gravitational singularity, Degree, Nirenberg and Matthaei experiment and Hausdorff distance. His studies deal with areas such as Extension, Mathematical analysis and Bounded operator as well as Combinatorics.

He works in the field of Mathematical analysis, focusing on Approximations of π in particular. His Omega research includes elements of Space, Lambda, Hausdorff space and Equivalence relation. He has included themes like Norm and Equivalence in his Pure mathematics study.

Between 2015 and 2021, his most popular works were:

  • Gagliardo-Nirenberg inequalities and non-inequalities: the full story (54 citations)
  • Gagliardo-Nirenberg inequalities and non-inequalities: the full story (54 citations)
  • Non-local functionals related to the total variation and connections with Image Processing (31 citations)

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

  • Mathematical analysis
  • Quantum mechanics
  • Geometry

Haim Brezis spends much of his time researching Sobolev space, Combinatorics, Omega, Non local and Function. His research brings together the fields of Maximal function and Sobolev space. His biological study spans a wide range of topics, including Type inequality, Nirenberg and Matthaei experiment, Mathematical analysis, Inequality and Negative number.

The Mathematical analysis study combines topics in areas such as Pointwise convergence, Pure mathematics and Regular polygon. His study in Interpolation inequality extends to Omega with its themes. His study connects Mathematical physics and Function.

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

Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert

H. Brézis.
(1973)

4818 Citations

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Haim Brezis.
(2010)

3366 Citations

Positive solutions of nonlinear elliptic equations involving critical sobolev exponents

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

3314 Citations

A Relation Between Pointwise Convergence of Functions and Convergence of Functionals

Haïm Brezis;Elliott Lieb;Elliott Lieb.
Proceedings of the American Mathematical Society (1983)

1906 Citations

Analyse fonctionnelle : théorie et applications

H. Brézis.
(1983)

1808 Citations

Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems

Antonio Ambrosetti;Haim Brezis;Giovanna Cerami.
Journal of Functional Analysis (1994)

1100 Citations

Ginzburg-Landau Vortices

Fabrice Bethuel;Haim Brezis;Frederic Helein.
(1994)

1001 Citations

Équations et inéquations non linéaires dans les espaces vectoriels en dualité

Haïm Brézis.
Annales de l'Institut Fourier (1968)

878 Citations

Blow-up solutions of some nonlinear elliptic problems

Haim Brezis;Juan Luis Vázquez.
Revista Matematica Complutense (1997)

648 Citations

Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)eu in two dimensions

Haïm Brezis;Frank Merle.
Communications in Partial Differential Equations (1991)

614 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.

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