Most cited papers in Nonlinear Partial Differential Equations
What are the most cited papers in Nonlinear Partial Differential Equations?
The most cited paper in Nonlinear Partial Differential Equations is "Dual variational methods in critical point theory and applications" (Antonio Ambrosetti, Paul H. Rabinowitz, 1973), with 4,419 citations. Next come "Hitchhikerʼs guide to the fractional Sobolev spaces" (4,369) and "Minimax Methods in Critical Point Theory with Applications to Differential Equations" (4,190).
Showing 50 of 100 papers. Every paper with more than 571 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Dual variational methods in critical point theory and applications Antonio Ambrosetti, Paul H. Rabinowitz · Journal of Functional Analysis | Dec 1973 | 4,419 |
| 2 | Hitchhikerʼs guide to the fractional Sobolev spaces Eleonora Di Nezza, Giampiero Palatucci, Enrico Valdinoci · Bulletin des Sciences Mathématiques | 29 Dec 2011 | 4,369 |
| 3 | Minimax Methods in Critical Point Theory with Applications to Differential Equations Paul H. Rabinowitz · Regional conference series in mathematics | Jul 1986 | 4,190 |
| 4 | Positive solutions of nonlinear elliptic equations involving critical sobolev exponents Haïm Brézis, Louis Nirenberg · Communications on Pure and Applied Mathematics | Jul 1983 | 2,942 |
| 5 | Symmetry and related properties via the maximum principle Basilis Gidas, Wei‐Ming Ni, Louis Nirenberg · Communications in Mathematical Physics | Oct 1979 | 2,934 |
| 6 | The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. Pierre‐Louis Lions · Annales de l Institut Henri Poincaré C Analyse Non Linéaire | Apr 1984 | 2,409 |
| 7 | An Extension Problem Related to the Fractional Laplacian Luis Caffarelli, Luis Silvestre · Communications in Partial Differential Equations | 8 Aug 2007 | 2,342 |
| 8 | An extension problem related to the fractional Laplacian Luis A. Caffarelli, Luís Silvestre | 2006 | 2,125 |
| 9 | A relation between pointwise convergence of functions and convergence of functionals Haïm Brézis, Élliott H. Lieb · Proceedings of the American Mathematical Society | Jul 1983 | 2,089 |
| 10 | Polar factorization and monotone rearrangement of vector‐valued functions Yann Brenier · Communications on Pure and Applied Mathematics | Jun 1991 | 1,719 |
| 11 | On the Spaces Lp(x)(Ω) and Wm,p(x)(Ω) Xianling Fan, Dun Zhao · Journal of Mathematical Analysis and Applications | Nov 2001 | 1,624 |
| 12 | On a class of nonlinear Schr�dinger equations Paul H. Rabinowitz · Zeitschrift für angewandte Mathematik und Physik | Mar 1992 | 1,585 |
| 13 | The concentration-compactness principle in the Calculus of Variations. The Locally compact case, part 2 Pierre‐Louis Lions · Annales de l Institut Henri Poincaré C Analyse Non Linéaire | Aug 1984 | 1,583 |
| 14 | THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION Félix Otto · Communications in Partial Differential Equations | 31 Jan 2001 | 1,567 |
| 15 | On the parabolic kernel of the Schrödinger operator Peter Li, Shing Tung Yau · Acta Mathematica | 1986 | 1,566 |
| 16 | Regularity for a more general class of quasilinear elliptic equations Peter Tolksdorf · Journal of Differential Equations | 1984 | 1,541 |
| 17 | Uniqueness of positive solutions of Δu−u+up=0 in Rn Man Kam Kwong · Archive for Rational Mechanics and Analysis | Sep 1989 | 1,352 |
| 18 | Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth Luis A. Caffarelli, Basilis Gidas, Joel Spruck · Communications on Pure and Applied Mathematics | Apr 1989 | 1,346 |
| 19 | Global and local behavior of positive solutions of nonlinear elliptic equations Basilis Gidas, Joel Spruck · Communications on Pure and Applied Mathematics | Jul 1981 | 1,319 |
| 20 | Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II Shmuel Agmon, Avron Douglis, Louis Nirenberg · Communications on Pure and Applied Mathematics | Feb 1964 | 1,318 |
| 21 | Boundary regularity for solutions of degenerate elliptic equations Gary M. Lieberman · Nonlinear Analysis | Nov 1988 | 1,306 |
| 22 | Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation Élliott H. Lieb · Studies in Applied Mathematics | Oct 1977 | 1,306 |
| 23 | Stress Concentration Factors R. E. Peterson, Robert K. Plunkett · Journal of Applied Mechanics | Mar 1975 | 1,304 |
| 24 | Regularity of the obstacle problem for a fractional power of the laplace operator Luís Silvestre · Communications on Pure and Applied Mathematics | 9 Aug 2006 | 1,281 |
| 25 | Progress in Nonlinear Differential Equations and their Applications Amandine Aftalion · HAL (Le Centre pour la Communication Scientifique Directe) | 2006 | 1,261 |
| 26 | Motion of level sets by mean curvature. I L. C. Evans, Joel Spruck · Journal of Differential Geometry | 1991 | 1,220 |
| 27 | The Yamabe problem John Michael Lee, Thomas H. Parker · Bulletin of the American Mathematical Society | 1987 | 1,186 |
| 28 | A Strong Maximum Principle for some quasilinear elliptic equations Juan-Luis V�zquez · Applied Mathematics & Optimization | Oct 1984 | 1,182 |
| 29 | C1 + α local regularity of weak solutions of degenerate elliptic equations Emmanuele DiBenedetto · Nonlinear Analysis | 1983 | 1,137 |
| 30 | Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems Antonio Ambrosetti, Haïm Brézis, G. Cerami · Journal of Functional Analysis | Jun 1994 | 1,083 |
| 31 | Non-linear elliptic and parabolic equations involving measure data Lucio Boccardo, Thierry Gallouët · Journal of Functional Analysis | Nov 1989 | 1,059 |
| 32 | Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus Guido Stampacchia · Annales de l’institut Fourier | 1965 | 1,042 |
| 33 | Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality Félix Otto, Cédric Villani · Journal of Functional Analysis | Jun 2000 | 979 |
| 34 | The local regularity of solutions of degenerate elliptic equations Eugene B. Fabes, Carlos E. Kenig, Raul Serapioni · Communications in Partial Differential Equations | 1982 | 948 |
| 35 | Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation Luis A. Caffarelli, Alexis Vasseur · Annals of Mathematics | 25 Apr 2010 | 946 |
| 36 | Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities Élliott H. Lieb | 2002 | 946 |
| 37 | Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system Yoshikazu Giga · Journal of Differential Equations | Apr 1986 | 910 |
| 38 | The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian Luis A. Caffarelli, Louis Nirenberg, Joel Spruck · Acta Mathematica | 1985 | 898 |
| 39 | Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics Vitaly Moroz, Jean Van Schaftingen · Journal of Functional Analysis | 28 Apr 2013 | 886 |
| 40 | Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds Alexander Asaturovich Grigor'yan · Bulletin of the American Mathematical Society | 19 Feb 1999 | 877 |
| 41 | The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary Xavier Ros‐Oton, Joaquim Serra · Journal de Mathématiques Pures et Appliquées | 13 Jun 2013 | 870 |
| 42 | Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds Jeff Cheeger, Mikhail Leonidovich Gromov, Michael Eugene Taylor · Journal of Differential Geometry | 1982 | 861 |
| 43 | On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ N Louis Jeanjean · Proceedings of the Royal Society of Edinburgh Section A Mathematics | 1999 | 858 |
| 44 | A priori bounds for positive solutions of nonlinear elliptic equations Basilis Gidas, Joel Spruck · Communications in Partial Differential Equations | 1981 | 849 |
| 45 | Local mountain passes for semilinear elliptic problems in unbounded domains Manuel del Pino, Patricio L. Felmer · Calculus of Variations and Partial Differential Equations | Feb 1996 | 847 |
| 46 | On the geometry of metric measure spaces Karl‐Theodor Sturm · Acta Mathematica | 2006 | 844 |
| 47 | Classification of solutions for an integral equation Wenxiong Chen, Congming Li, Biao Ou · Communications on Pure and Applied Mathematics | 19 Dec 2005 | 844 |
| 48 | Existence of solutions for p(x)-Laplacian Dirichlet problem Xianling Fan, Qihu Zhang · Nonlinear Analysis | 28 Dec 2002 | 837 |
| 49 | Regularity and existence of solutions of elliptic equations with p,q-growth conditions Paolo Marcellini · Journal of Differential Equations | Mar 1991 | 826 |
| 50 | Backward stochastic differential equations and partial differential equations with quadratic growth Magdalena Kobylanski · The Annals of Probability | Apr 2000 | 815 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.