Louis Nirenberg

Louis Nirenberg ( born February 28, 1925 in Hamilton, Ontario ) is a Canadian mathematician who researches differential equations, especially in the field of partial.

Life

Nirenberg attended high school in Montreal and studied at McGill University ( BA 1945), then at the New York University, where he studied with Richard Courant and Kurt Friedrichs, 1947 received his master's degree and in 1949 his doctorate under James Stoker was ( he broke in the Weyl embedding problem in differential geometry ). 1951/52, he was in Zurich at Heinz Hopf and in Göttingen, among others, with Franz Rellich. Nirenberg was a professor at the Courant Institute of Mathematical Sciences, where he remained for the rest of his career until his retirement in 1999, and at times was its director. Nirenberg has supervised more than 40 doctoral students there. In 1958 he was at the Institute for Advanced Study.

Work

Nirenberg is regarded as one of the outstanding analysts of the 20th century. He provided fundamental contributions to the theory of linear and nonlinear partial differential equations and their applications in differential geometry and complex analysis.

With Fritz John, he began the study of functions with "bounded mean oscillation " ( BMO ):

Focusing on the integration and mean values ​​are considered in cubes with volume and a constant. They showed that of " exponential class " (with a constant ):

With Luis Caffarelli and Robert V. Kohn, he examined the possible singularities in the Navier -Stokes equations ( a problem that is largely still open and has been included in the list of Millennium Problems of the Clay Mathematics Institute ). It characterized by the rate of concentration of the energy density of the possible singularities, and showed that the 1-dimensional Hausdorff measure the singular points disappear in three spatial dimensions. They built on the work of V. Scheffer on from the mid- 1970s.

With his doctoral A. Newlander he characterized complex structures under almost complex structures ( set of Newlander - Nirenberg ). They showed that integrability, generalize the Cauchy- Riemann equations in the case, are not only necessary but also sufficient. How Nirenberg recalls, he was to this problem by André Weil and Shiing - Shen inspired Chern - especially since called for dealing with partial differential equations employing analysts to out, for once in his view, really fundamental problems, in this case, a long open problem of of complex analysis to tackle. With the set of Newlander - Nirenberg he proved with Kodaira and Spencer Donald existence theorems on the deformation of complex structures.

In a work from 1965 with Joseph Kohn, he led a pseudo-differential operators .. According to his own statements, this was a by- product of their work over the Neumann problem that demanded hitherto unpublished results on the algebra of singular integral operators.

Features the work of Nirenberg is ( as with his teacher, Kurt Friedrichs, the Nirenberg described in a 2002 interview as the mathematician who him most affected ) are often an artful application of inequalities, for example, in working with Avron Douglis and Shmuel Agmon over assessments of boundary value problems of elliptic partial differential equations, in which they built on the work of Juliusz Schauder. He does not see himself as the founder of theory - building, but as a problem - solver.

Honors and Memberships

He has received numerous honors and awards, including the Swedish Crafoord Prize 1982 ( the first recipient ) and the National Medal of Science, and the first Chern Medal of the IMU in 2010. 1962 he gave a plenary lecture at the International Congress of Mathematicians in Stockholm ( Some Aspects of linear and nonlinear partial differential equations ). He was Guggenheim Fellow (1966) and Sloan Fellow and received the " Award of Excellence in Science and Technology" of the City of New York. In 1994 he received the Leroy P. Steele Prize of the American Mathematical Society. The Bôcher Memorial Prize of the AMS he had previously received in 1959 for " outstanding achievements in mathematical analysis ". For 2014, the Leroy P. Steele Prize him the Ukrainian was awarded for his work with Robert V. Kohn and Caffarelli of 1982. He is a member of the National Academy of Sciences of the United States, the American Academy of Arts and Sciences, the American Philosophical Society, and Lombard Academy of Sciences, the Paris Academie des Sciences and the Italian Accademia dei Lincei. He is a Fellow of the American Mathematical Society.

Writings

• Lectures on linear partial differential equations. In: Conference Board of the Mathematical Sciences of the AMS. American Mathematical Society, Providence (Rhode Iceland ) 1973.
• Functional Analysis. Courant Institute in 1961.
• Topics in Nonlinear Functional Analysis. Courant Institute in 1974.
• Partial differential equations in the first half of the century, in Jean -Paul Pier Development of mathematics 1900-1950, Birkhäuser 1994