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
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.
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.
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.
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.
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Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
S. Agmon;A. Douglis;L. Nirenberg.
Communications on Pure and Applied Mathematics (1959)
Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
Haïm Brezis;Louis Nirenberg.
Communications on Pure and Applied Mathematics (1983)
Symmetry and related properties via the maximum principle
B. Gidas;Wei Ming Ni;L. Nirenberg.
Communications in Mathematical Physics (1979)
On functions of bounded mean oscillation
F. John;L. Nirenberg.
Communications on Pure and Applied Mathematics (1961)
On elliptic partial differential equations
Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze (1959)
Partial regularity of suitable weak solutions of the navier‐stokes equations
L. Caffarelli;R. Kohn;L. Nirenberg.
Communications on Pure and Applied Mathematics (1982)
Topics in Nonlinear Functional Analysis
First order interpolation inequalities with weights
L. Caffarelli;R. Kohn;L. Nirenberg.
Compositio Mathematica (1984)
Complex Analytic Coordinates in Almost Complex Manifolds
A. Newlander;L. Nirenberg.
Annals of Mathematics (1957)
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)
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