Avner Friedman

25.7k total citations · 3 hit papers
430 papers, 17.6k citations indexed

About

Avner Friedman is a scholar working on Computational Theory and Mathematics, Applied Mathematics and Mathematical Physics. According to data from OpenAlex, Avner Friedman has authored 430 papers receiving a total of 17.6k indexed citations (citations by other indexed papers that have themselves been cited), including 154 papers in Computational Theory and Mathematics, 144 papers in Applied Mathematics and 101 papers in Mathematical Physics. Recurrent topics in Avner Friedman's work include Advanced Mathematical Modeling in Engineering (126 papers), Nonlinear Partial Differential Equations (73 papers) and Mathematical Biology Tumor Growth (58 papers). Avner Friedman is often cited by papers focused on Advanced Mathematical Modeling in Engineering (126 papers), Nonlinear Partial Differential Equations (73 papers) and Mathematical Biology Tumor Growth (58 papers). Avner Friedman collaborates with scholars based in United States, China and Spain. Avner Friedman's co-authors include Luis Caffarelli, Wenrui Hao, Bei Hu, Bryce McLeod, Emmanuele DiBenedetto, Fernando Reitich, Michael Vogelius, Hans Wilhelm Alt, Xinfu Chen and Xiulan Lai and has published in prestigious journals such as Proceedings of the National Academy of Sciences, Circulation and PLoS ONE.

In The Last Decade

Avner Friedman

421 papers receiving 15.1k citations

Hit Papers

Partial Differential Equa... 1964 2026 1984 2005 1964 1982 1985 500 1000 1.5k 2.0k 2.5k
What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

  1. Partial Differential Equations of Parabolic Type
    1964 2.8k citations Avner Friedman profile →
  2. Variational principles and free-boundary problems
    1982 646 citations Avner Friedman profile →
  3. Blow-up of positive solutions of semilinear heat equations
    1985 433 citations Avner Friedman Indiana University Mathematics Journal profile →

Author Peers

Peers are selected by citation overlap in the author's most active subfields. citations · hero ref

Author Last Decade Papers Cites
Avner Friedman 6.8k 6.5k 4.4k 3.0k 2.0k 430 17.6k
Shiing-Shen Chern 6.9k 1.0× 11.5k 1.8× 7.0k 1.6× 1.3k 0.4× 3.6k 1.8× 88 23.4k
V. A. Solonnikov 3.6k 0.5× 4.9k 0.7× 2.8k 0.6× 893 0.3× 1.9k 0.9× 159 8.0k
Michael G. Crandall 6.2k 0.9× 7.6k 1.2× 3.0k 0.7× 1.8k 0.6× 2.4k 1.2× 99 14.6k
Neil S. Trudinger 9.7k 1.4× 14.4k 2.2× 6.3k 1.4× 818 0.3× 1.2k 0.6× 125 19.6k
Pierre‐Louis Lions 8.9k 1.3× 12.6k 1.9× 8.3k 1.9× 1.6k 0.5× 2.6k 1.3× 192 23.0k
Jack K. Hale 4.6k 0.7× 6.2k 0.9× 2.6k 0.6× 3.0k 1.0× 9.1k 4.6× 166 23.9k
Hans F. Weinberger 2.8k 0.4× 3.7k 0.6× 2.2k 0.5× 1.7k 0.6× 962 0.5× 95 9.4k
Haı̈m Brezis 12.6k 1.9× 14.9k 2.3× 8.0k 1.8× 901 0.3× 2.6k 1.3× 182 21.0k
David Gilbarg 7.3k 1.1× 9.7k 1.5× 4.9k 1.1× 754 0.2× 1.1k 0.5× 20 14.5k
Juncheng Wei 5.1k 0.8× 7.0k 1.1× 4.5k 1.0× 789 0.3× 855 0.4× 534 12.8k

Countries citing papers authored by Avner Friedman

Since Specialization
Citations

This map shows the geographic impact of Avner Friedman's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Avner Friedman with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Avner Friedman more than expected).

Fields of papers citing papers by Avner Friedman

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Avner Friedman. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Avner Friedman. The network helps show where Avner Friedman may publish in the future.

Co-authorship network of co-authors of Avner Friedman

This figure shows the co-authorship network connecting the top 25 collaborators of Avner Friedman. A scholar is included among the top collaborators of Avner Friedman based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Avner Friedman. Avner Friedman is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Friedman, Avner. (2010). What Is Mathematical Biology and How Useful Is It. 11(1). 21010–21010. 11 indexed citations
2.
Friedman, Avner & Fernando Reitich. (1991). The Stefan Problem with Small Surface Tension. Transactions of the American Mathematical Society. 328(2). 465–465. 6 indexed citations
3.
Friedman, Avner & Fernando Reitich. (1991). The Stefan problem with small surface tension. Transactions of the American Mathematical Society. 328(2). 465–515. 16 indexed citations
4.
Friedman, Avner & Luc Oswald. (1988). The Blow-up Surface for Nonlinear Wave Equations with Small Spatial Velocity. Transactions of the American Mathematical Society. 308(1). 349–349. 1 indexed citations
5.
Caffarelli, Luis & Avner Friedman. (1986). The Blow-Up Boundary for Nonlinear Wave Equations. Transactions of the American Mathematical Society. 297(1). 223–223. 13 indexed citations
6.
Alt, Hans Wilhelm, Luis Caffarelli, & Avner Friedman. (1984). Variational problems with two phases and their free boundaries. Transactions of the American Mathematical Society. 282(2). 431–461. 254 indexed citations
7.
Friedman, Avner & Daniel R. Phillips. (1984). The Free Boundary of a Semilinear Elliptic Equation. Transactions of the American Mathematical Society. 282(1). 153–153. 9 indexed citations
8.
Friedman, Avner & Bruce Turkington. (1981). Vortex rings: existence and asymptotic estimates. Transactions of the American Mathematical Society. 268(1). 1–1. 58 indexed citations
9.
Friedman, Avner, et al.. (1980). The free boundary for elastic-plastic torsion problems. Transactions of the American Mathematical Society. 257(2). 411–425. 3 indexed citations
10.
Caffarelli, Luis & Avner Friedman. (1979). Continuity of the density of a gas flow in a porous medium. Transactions of the American Mathematical Society. 252(0). 99–113. 62 indexed citations
11.
Friedman, Avner & Mark A. Pinsky. (1973). Dirichlet problem for degenerate elliptic equations. Transactions of the American Mathematical Society. 186. 359–359. 9 indexed citations
12.
Friedman, Avner. (1968). The Stefan problem in several space variables. Transactions of the American Mathematical Society. 133(1). 51–87. 156 indexed citations
13.
Friedman, Avner. (1968). The Stefan Problem in Several Space Variables. Transactions of the American Mathematical Society. 133(1). 51–51. 33 indexed citations
14.
Friedman, Avner & Walter Littman. (1962). Bodies for which harmonic functions satisfy the mean value property. Transactions of the American Mathematical Society. 102(1). 147–166. 5 indexed citations
15.
Friedman, Avner. (1961). A New Proof and Generalizations of the Cauchy-Kowalewski Theorem. Transactions of the American Mathematical Society. 98(1). 1–1. 9 indexed citations
16.
Friedman, Avner. (1961). Function-theoretic characterization of Einstein spaces and harmonic spaces. Transactions of the American Mathematical Society. 101(2). 240–258. 6 indexed citations
17.
Friedman, Avner. (1961). Function-Theoretic Characterization of Einstein Spaces and Harmonic Spaces. Transactions of the American Mathematical Society. 101(2). 240–240. 2 indexed citations
18.
Friedman, Avner. (1960). Remarks on Stefan-Type Free Boundary Problems for Parabolic Equations. Indiana University Mathematics Journal. 9(6). 885–903. 20 indexed citations
19.
Friedman, Avner. (1960). On Quasi-Linear Parabolic Equations of the Second Order II. Indiana University Mathematics Journal. 9(4). 539–556. 10 indexed citations
20.
Friedman, Avner. (1959). Generalized Heat Transfer between Solids and Gases under Nonlinear Boundary Conditions. Indiana University Mathematics Journal. 8(2). 161–183. 29 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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