What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Quantum mechanics
- Partial differential equation
The scientist’s investigation covers issues in Mathematical analysis, Numerical analysis, Applied mathematics, Humanities and Variational inequality.
His Mathematical analysis and Boundary value problem, Hyperbolic partial differential equation, Laplace transform, Calculus of variations and Iterated function investigations all form part of his Mathematical analysis research activities.
His work deals with themes such as Combinatorics, Schrödinger equation, Banach space, Scalar and Existence theorem, which intersect with Boundary value problem.
Jacques-Louis Lions works mostly in the field of Numerical analysis, limiting it down to concerns involving Industrial engineering and, occasionally, Cover and Computation.
His study in Applied mathematics is interdisciplinary in nature, drawing from both Partial differential equation, Asymptotic analysis and Differential equation.
His work carried out in the field of Partial differential equation brings together such families of science as Scale, Mathematical proof, Weak convergence, Asymptotic expansion and Asymptotic homogenization.
His most cited work include:
- Quelques méthodes de résolution des problèmes aux limites non linéaires (5337 citations)
- Non-homogeneous boundary value problems and applications (4655 citations)
- Asymptotic analysis for periodic structures (4333 citations)
What are the main themes of his work throughout his whole career to date?
His primary scientific interests are in Mathematical analysis, Applied mathematics, Numerical analysis, Controllability and Partial differential equation.
His Mathematical analysis research is multidisciplinary, relying on both Boundary and Nonlinear system.
His Applied mathematics research includes themes of Mathematical optimization and Differential equation.
His biological study spans a wide range of topics, including Computational science, Finite element method and Calculus.
As part of his studies on Partial differential equation, Jacques-Louis Lions frequently links adjacent subjects like Pure mathematics.
His Neumann boundary condition and Dirichlet problem investigations are all subjects of Boundary value problem research.
He most often published in these fields:
- Mathematical analysis (25.94%)
- Applied mathematics (21.70%)
- Numerical analysis (14.62%)
What were the highlights of his more recent work (between 1996-2017)?
- Applied mathematics (21.70%)
- Mathematical analysis (25.94%)
- Numerical analysis (14.62%)
In recent papers he was focusing on the following fields of study:
Applied mathematics, Mathematical analysis, Numerical analysis, Controllability and Nonlinear system are his primary areas of study.
Jacques-Louis Lions has researched Applied mathematics in several fields, including Partial differential equation, Uniqueness, Bilinear form and Control theory.
His study explores the link between Mathematical analysis and topics such as Finite element method that cross with problems in Integral equation and Dirichlet problem.
His study in the field of Numerical stability is also linked to topics like Volume.
His research in Controllability intersects with topics in Helmholtz equation and Distributed parameter system.
He has included themes like Elliptic operator and Optimal control in his Boundary value problem study.
Between 1996 and 2017, his most popular works were:
- Résolution d'EDP par un schéma en temps « pararéel » (296 citations)
- Mathematical Analysis and Numerical Methods for Science and Technology: Volume 4 Integral Equations and Numerical Methods (161 citations)
- Two-grid finite-element schemes for the transient Navier-Stokes problem (96 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Partial differential equation
- Quantum mechanics
Jacques-Louis Lions spends much of his time researching Mathematical analysis, Applied mathematics, Numerical analysis, Boundary value problem and Controllability.
His work carried out in the field of Mathematical analysis brings together such families of science as Finite element method, Galerkin method, Scale and Boundary.
Jacques-Louis Lions focuses mostly in the field of Applied mathematics, narrowing it down to matters related to Partial differential equation and, in some cases, Optimal control, Domain decomposition methods, Controllability Gramian and Control.
His Numerical analysis research is multidisciplinary, incorporating elements of Mechanics, Numerical partial differential equations and Calculus.
His studies in Boundary value problem integrate themes in fields like Well-posed problem, Algebra, Hyperbolic partial differential equation, Nonlinear system and Maxwell's equations.
His Controllability research is multidisciplinary, incorporating perspectives in Wave equation, State, Distributed parameter system and Domain.
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