L. E. Payne

11.1k citations

282 papers · 7.7k indexed · 1 hit paper · h-index 44

Impact in

Applied Mathematics top 0.05%
- Nonlinear Partial Differential Equations
Mathematical Physics top 0.1%
- Numerical methods in inverse problems
- Advanced Mathematical Physics Problems

Papers in ⓘ

Applied Mathematics 115
- Nonlinear Partial Differential Equations 55
- Differential Equations and Boundary Problems 31
Computational Theory and Mathematics 154
- Advanced Mathematical Modeling in Engineering 140
- Contact Mechanics and Variational Inequalities 28

Co-authors: Hans F. Weinberger (11 shared papers)R. J. Knops (23 shared papers)D. H. Sattinger (1 shared paper)Brian Straughan (23 shared papers)G. A. Philippin (32 shared papers)Philip Schaefer (22 shared papers)Junqiang Song (29 shared papers)Howard A. Levine (11 shared papers)
Journals: Mathematical Methods in the Applied Sciences (28 papers)Journal of Mathematical Analysis and Applications (24 papers)Zeitschrift für angewandte Mathematik und Physik (19 papers)Archive for Rational Mechanics and Analysis (19 papers)Nonlinear Analysis (13 papers)
Partner nations: United States United Kingdom Canada

In The Last Decade

L. E. Payne

269 papers receiving 6.5k citations

Hit Papers

align trajectories log scale

Saddle points and instability of nonlinear hyperbolic equations 1975 · 610 citations

Peers

Countries citing papers authored by L. E. Payne

Since Specialization

Citations

This map shows the geographic impact of L. E. Payne's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by L. E. Payne with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites L. E. Payne more than expected).

Fields of papers citing papers by L. E. Payne

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by L. E. Payne. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by L. E. Payne. The network helps show where L. E. Payne may publish in the future.

Co-authors

The 25 scholars most cited alongside L. E. Payne, linked wherever they have co-authored with each other. Click a name or a connecting line to browse the papers they share.

Border = papers with L. E. Payne Line = papers co-authored together L. E. Payne links everyone, so they are left out of the graph.

All Works

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20 of 20 papers shown

Showing the 20 most-cited of 282 papers — load more, or switch the sort, to bring in the rest.

#	Work
1	Saddle points and instability of nonlinear hyperbolic equations Israel Journal of Mathematics ·L. E. Payne, D. H. Sattinger Hit paper breakdown →	1975	610
2	An optimal Poincaré inequality for convex domains Archive for Rational Mechanics and Analysis ·L. E. Payne, Hans F. Weinberger	1960	414
3	Isoperimetric Inequalities and Their Applications SIAM Review ·L. E. Payne	1967	237
4	On the Ratio of Consecutive Eigenvalues Journal of Mathematics and Physics ·L. E. Payne, Georg Pólya, Hans F. Weinberger	1956	191
5	The Stokes flow problem for a class of axially symmetric bodies Journal of Fluid Mechanics ·L. E. Payne, William H. Pell	1960	184
6	Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time Journal of Differential Equations ·Howard A. Levine, L. E. Payne	1974	159
7	Uniqueness Theorems in Linear Elasticity CERN Document Server (European Organization for Nuclear Research) ·R. J. Knops, L. E. Payne	1971	141
8	New bounds for solutions of second order elliptic partial differential equations Pacific Journal of Mathematics ·L. E. Payne, Hans F. Weinberger	1958	111
9	Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions Journal de Mathématiques Pures et Appliquées ·L. E. Payne, Brian Straughan	1998	110
10	Decay estimates for the constrained elastic cylinder of variable cross section Quarterly of Applied Mathematics ·James N. Flavin, R. J. Knops, L. E. Payne	1989	106
11	Lower bounds for blow-up time in parabolic problems under Dirichlet conditions Journal of Mathematical Analysis and Applications ·L. E. Payne, Philip Schaefer	2006	98
12	Spatial decay estimates in transient heat conduction Quarterly of Applied Mathematics ·Cornelius O. Horgan, L. E. Payne, Lewis Wheeler	1984	96
13	Convergence and Continuous Dependence for the Brinkman–Forchheimer Equations Studies in Applied Mathematics ·L. E. Payne, Brian Straughan	1999	95
14	On Korn's inequality Archive for Rational Mechanics and Analysis ·L. E. Payne, Hans F. Weinberger	1961	92
15	Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences ·L. E. Payne, Junqiang Song, Brian Straughan	1999	86
16	Lower bounds for blow-up time in parabolic problems under Neumann conditions Applicable Analysis ·L. E. Payne, Philip Schaefer	2006	84
17	Inhibition of growth hormone-releasing factor suppresses both sleep and growth hormone secretion in the rat Brain Research ·F. Obál, L. E. Payne, Levente Kapás, Mark R. Opp, James M. Krueger	1991	78
18	Blow-up phenomena for some nonlinear parabolic problems Nonlinear Analysis ·L. E. Payne, G. A. Philippin, Philip Schaefer	2007	75
19	Bounds in the Neumann problem for second order uniformly elliptic operators Pacific Journal of Mathematics ·James H. Bramble, L. E. Payne	1962	75
20	On inequalities of Korn, Friedrichs and Babuška-Aziz Archive for Rational Mechanics and Analysis ·Cornelius O. Horgan, L. E. Payne	1983	73

About L. E. Payne

L. E. Payne is a scholar working on Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics, Numerical Analysis and Computational Mechanics, having authored 282 papers that have together received 7.7k indexed citations. Recurring topics across this work include Advanced Mathematical Modeling in Engineering (140 papers), Nonlinear Partial Differential Equations (55 papers), Numerical methods in inverse problems (51 papers), Stability and Controllability of Differential Equations (50 papers), Differential Equations and Boundary Problems (31 papers), Contact Mechanics and Variational Inequalities (28 papers), Elasticity and Material Modeling (23 papers) and Advanced Mathematical Physics Problems (21 papers). The work is most often cited by research in Applied Mathematics (3.2k citations), Mathematical Physics (2.7k citations), Computational Theory and Mathematics (3.8k citations), Numerical Analysis (641 citations) and Computational Mechanics (1.6k citations). L. E. Payne has collaborated with scholars based in United States, United Kingdom and Canada. Frequent co-authors include Hans F. Weinberger, R. J. Knops, D. H. Sattinger, Brian Straughan, G. A. Philippin, Philip Schaefer, Junqiang Song, Howard A. Levine, Cornelius O. Horgan and William H. Pell. Their work appears in journals such as Mathematical Methods in the Applied Sciences, Journal of Mathematical Analysis and Applications, Zeitschrift für angewandte Mathematik und Physik, Archive for Rational Mechanics and Analysis and Nonlinear Analysis.

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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