What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Partial differential equation
- Geometry
His main research concerns Mathematical analysis, Upper and lower bounds, Boundary value problem, Complex system and Partial differential equation.
His Mathematical analysis study frequently links to related topics such as Stress.
The concepts of his Upper and lower bounds study are interwoven with issues in Non linearite, Differential inequalities and Parallelepiped.
His study focuses on the intersection of Boundary value problem and fields such as Heat equation with connections in the field of Mixed boundary condition and Free boundary problem.
L. E. Payne works mostly in the field of Partial differential equation, limiting it down to topics relating to Initial value problem and, in certain cases, Dirichlet conditions and Dirichlet problem.
His Elliptic partial differential equation study combines topics in areas such as Cauchy problem, Cauchy's convergence test, Cauchy matrix, Cauchy boundary condition and Hyperbolic partial differential equation.
His most cited work include:
- An optimal Poincaré inequality for convex domains (508 citations)
- On Korn's inequality (127 citations)
- Decay estimates for the constrained elastic cylinder of variable cross section (106 citations)
What are the main themes of his work throughout his whole career to date?
Mathematical analysis, Boundary value problem, Partial differential equation, Upper and lower bounds and Thermal conduction are his primary areas of study.
His work often combines Mathematical analysis and Exponential decay studies.
His Boundary value problem research also works with subjects such as
- Exponential growth that intertwine with fields like Lateral surface,
- Cylinder and related Parabolic cylinder function.
His study looks at the intersection of Upper and lower bounds and topics like Dirichlet problem with Elliptic curve.
L. E. Payne has included themes like Heat kernel and Heat flux in his Thermal conduction study.
His biological study spans a wide range of topics, including Split-step method and Instability.
He most often published in these fields:
- Mathematical analysis (88.31%)
- Boundary value problem (31.17%)
- Partial differential equation (18.18%)
What were the highlights of his more recent work (between 2000-2013)?
- Mathematical analysis (88.31%)
- Boundary value problem (31.17%)
- Upper and lower bounds (12.34%)
In recent papers he was focusing on the following fields of study:
L. E. Payne focuses on Mathematical analysis, Boundary value problem, Upper and lower bounds, Heat equation and Partial differential equation.
The various areas that he examines in his Mathematical analysis study include Thermal conduction, Differential inequalities and Heat flux.
His Boundary value problem research includes themes of Cylinder, Geometry, Initial value problem and Zero.
The study incorporates disciplines such as Non linearite, Robin boundary condition and Applied mathematics in addition to Upper and lower bounds.
His Heat equation research is multidisciplinary, incorporating elements of Pointwise and Boundary, Mixed boundary condition.
As part of the same scientific family, L. E. Payne usually focuses on Partial differential equation, concentrating on Dirichlet problem and intersecting with Existence theorem, Thermoelastic damping, Hyperbolic partial differential equation, Heat transfer and Traction.
Between 2000 and 2013, his most popular works were:
- Lower bounds for blow-up time in parabolic problems under Dirichlet conditions (103 citations)
- Lower bounds for blow-up time in parabolic problems under Neumann conditions (94 citations)
- Blow-up phenomena for some nonlinear parabolic problems (83 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Partial differential equation
- Geometry
L. E. Payne spends much of his time researching Mathematical analysis, Upper and lower bounds, Partial differential equation, Heat equation and Boundary value problem.
His Mathematical analysis research integrates issues from Geometry, Double diffusive convection and Structural stability.
His biological study spans a wide range of topics, including Non linearite and Differential inequalities.
L. E. Payne has included themes like Dirichlet problem and Initial value problem in his Partial differential equation study.
As part of one scientific family, L. E. Payne deals mainly with the area of Heat equation, narrowing it down to issues related to the Mixed boundary condition, and often Neumann boundary condition.
His Pointwise study incorporates themes from Differential operator, Pure mathematics and Parabolic cylinder function.
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