What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Partial differential equation
- Geometry
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.
His most cited work include:
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I (3354 citations)
- Symmetry and related properties via the maximum principle (2334 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?
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.
He most often published in these fields:
- Mathematical analysis (58.06%)
- Pure mathematics (23.39%)
- Elliptic partial differential equation (19.35%)
What were the highlights of his more recent work (between 2000-2016)?
- Mathematical analysis (58.06%)
- Pure mathematics (23.39%)
- Hopf lemma (5.65%)
In recent papers he was focusing on the following fields of study:
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.
Between 2000 and 2016, his most popular works were:
- Topics in Nonlinear Functional Analysis (790 citations)
- Properties of Solutions of Ordinary Differential Equations in Banach Space (290 citations)
- Estimates for elliptic systems from composite material (230 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Partial differential equation
- Geometry
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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