## ⓘ Louis Nirenberg

Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.

He made fundamental contributions to linear and nonlinear partial differential equations PDEs and their application to complex analysis and geometry. His contributions include the Gagliardo–Nirenberg interpolation inequality, which is important in the solution of the elliptic partial differential equations that arise in many areas of mathematics, and the formalization of the bounded mean oscillation known as John–Nirenberg space, which is used to study the behavior of both elastic materials and games of chance known as martingales. His other achievements include the solution to long-standing problems of Weyl and Minkowski, relating to the embedding of a 2-sphere and curvature, respectively; the theory of pseudo-differential operators initiated along with Joseph J. Kohn, the Newlander-Nirenberg theorem of complex structures, Vanishing Mean Oscillation VMO, the symmetries of solutions of PDEs along with Gidas and Ni, among many others.

Nirenbergs work on PDEs has been described as "about the best thats been done" as of 2002 towards solving the Navier–Stokes existence and smoothness problem of fluid mechanics, which is a Millennium Prize Problem.

## 1. Biography

Nirenberg was born in Hamilton, Ontario, and attended Baron Byng High School. He studied as an undergraduate at McGill University, completing there his B.S. in both mathematics and physics in 1945. He obtained his doctorate from New York University in 1949 under the direction of James Stoker. He subsequently became a professor at the Courant Institute of Mathematical Sciences at New York University. He was also conferred the degree of Doctor of Science, honoris causa, at the University of British Columbia in 2010.

He received many honours and awards, including the Bocher Memorial Prize 1959, the Jeffery–Williams Prize 1987, the Steele Prize 1994 and 2014, the National Medal of Science 1995, and was the inaugural recipient of both the Crafoord Prize 1982, shared with Vladimir Arnold and the Chern Medal 2010. In 2015 he was awarded the Abel Prize along with John Nash. He was a fellow of the American Mathematical Society.

On 26 January 2020, it was announced that Nirenberg had died age 94.

## 2. Selected works

- Topics in Nonlinear Functional Analysis. Courant Institute 1974.
- Functional Analysis. Courant Institute 1961.
- Lectures on linear partial differential equations. In: Conference Board of the Mathematical Sciences of the AMS. American Mathematical Society, Providence Rhode Island 1973.
- Partial differential equations in the first half of the century, in Jean-Paul Pier Development of mathematics 1900–1950, Birkhauser 1994
- Caffarelli, Luis; Kohn, Robert; Nirenberg, Louis 1982, "Partial regularity of suitable weak solutions of the navier-stokes equations", Communications on Pure and Applied Mathematics, 35 6: 771–831, doi:10.1002/cpa.3160350604

- theory of elliptic partial differential equations. It was proposed by Louis Nirenberg and Emilio Gagliardo. The inequality concerns functions u: Rn R.
- Nirenberg is the surname of the following people: David Nirenberg American historian Louis Nirenberg born 1925 Canadian - born Canadian - American mathematician
- Marshall Warren Nirenberg April 10, 1927 January 15, 2010 was an American biochemist and geneticist. He shared a Nobel Prize in Physiology or Medicine
- called John Nirenberg space, after Fritz John and Louis Nirenberg who introduced and studied it for the first time. According to Nirenberg 1985, p. 703
- non - linear partial differential equations, specially the ones with Louis Nirenberg and Luis Caffarelli, where they obtained partial results about the
- the original on 2010 - 08 - 25. Retrieved Aug 22, 2010. Chern Medal Louis Nirenberg ICM 2010. August 19, 2010. Retrieved Aug 22, 2010. Chern Medal Award
- Theory for Periodic Dissipative Wave Equations, was supervised by Louis Nirenberg In 2007, he was made a Fellow of the Royal Society of Canada and he
- 1958 1966 Kurt O. Friedrichs 1966 1967 Jurgen Moser 1967 1970 Louis Nirenberg 1970 1972 Peter Lax 1972 1980 S. R. Srinivasa Varadhan 1980 1984
- isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr
- in the design of American stealth - aircraft F - 117 and B - 2. In 1953 Louis Nirenberg published the solutions of two long standing open problems, the Weyl

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