Applied Mathematics papers

Pofolia’s corpus holds 61 papers from Applied Mathematics (2012–2026), each with a short summary. Below, the 20 most-cited, then the most recently added.

At a glance

• Most cited: Stochastic Equations in Infinite Dimensions (2014, 4,106 citations).
• The 20 papers listed have 25,550 citations between them.
• 5 of the 5 with a known journal quartile appeared in a Q1 journal.
• 4 have a free full text (open access).
• Most frequent journals: Cambridge University Press eBooks, arXiv (Cornell University), Annual Review of Statistics and Its Application.
• Published between 2012 and 2026.

Most cited

Ranked by citation count. Because citations accumulate over time, this list naturally leans towards work published a few years ago; for where the field is now, see “recently added”. How to read the signals

• Stochastic Equations in Infinite Dimensions

  Cambridge University Press eBooks · 2014 · FWCI 45.41 · 4,106 citations

  This second edition of a book provides a systematic and self-contained presentation of fundamental results on stochastic evolution equations in infinite-dimensional spaces, such as Hilbert and Banach spaces.

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• Análisis Comparativo y Refutación Determinista de la Incertidumbre Cuántica Óptica de Fluidos en la Variedad RP3 vs. Ortodoxia Probabilística

  Open MIND · 2026 · 2,565 citations

  A new deterministic model of quantum vacuum interactions, based on classical collision mechanics in a viscoelastic medium, accurately predicts solar neutrino detection rates, refuting probabilistic quantum field theories.

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• Hypersonic and high temperature gas dynamics

  2013 · FWCI 159.14 · 2,188 citations

  This document outlines a comprehensive theoretical framework for understanding hypersonic and high-temperature gas dynamics, covering both inviscid and viscous flow regimes.

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• Nonlinear Potential Theory of Degenerate Elliptic Equations

  2018 · FWCI 117.30 · 1,799 citations

  This text provides a self-contained treatment of the nonlinear potential theory of superharmonic functions, suitable for advanced students.

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• Modern Compressible Flow: With Historical Perspective

  2020 · FWCI 86.92 · 1,597 citations

  This work presents a comprehensive overview of compressible flow, tracing its historical development and covering fundamental principles and advanced topics.

• Monotone Operators in Banach Space and Nonlinear Partial Differential Equations

  Mathematical surveys and monographs · 2013 · FWCI 21.47 · 1,206 citations

  This work introduces monotone operators in Banach spaces as a foundational tool for solving nonlinear partial differential equations (PDEs). It covers stationary and evolution problems, including nonlinear Cauchy problems.

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• Elasticities and the Inverse Hyperbolic Sine Transformation

  Oxford Bulletin of Economics and Statistics · 2019 · Q1 · FWCI 133.92 · 1,115 citations

  Applied econometricians can now derive precise elasticities when using the inverse hyperbolic sine (arcsinh) transformation, a common practice that allows retaining zero-valued observations.

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• Group Invariant Scattering

  Communications on Pure and Applied Mathematics · 2012 · Q1 · SJR 4.00 · FWCI 43.68 · 1,039 citations

  This paper constructs translation-invariant operators that are Lipschitz-continuous to diffeomorphism actions, enabling robust feature extraction from data.

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• Orthogonal Polynomials of Several Variables

  Cambridge University Press eBooks · 2014 · FWCI 13.66 · 1,008 citations

  This revised edition of a comprehensive text introduces orthogonal polynomials with modern concepts and notation, blending classical analysis with symmetry group theory.

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• On the rate of convergence in Wasserstein distance of the empirical\n measure

  arXiv (Cornell University) · 2013 · 970 citations · Open access

  This paper establishes new non-asymptotic bounds and concentration inequalities for the convergence rate of empirical measures to their true distribution in Wasserstein distance, for any order p > 0 and dimension d >= 1.

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• Convex Bodies The Brunn-MinkowskiTheory

  Cambridge University Press eBooks · 2013 · FWCI 6.54 · 957 citations

  This monograph offers a comprehensive introduction to convex bodies, focusing on the Brunn-Minkowski theory and its applications to volume and surface area. The second edition significantly expands on recent developments, including new chapters on valuations, Lp Brunn-Minkowski theory, and affine constructions.

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• Difference Equations and Inequalities: Theory, Methods, and Applications

  2019 · FWCI 39.11 · 948 citations

  This abstract outlines a broad scope of topics within the theory and application of difference equations and inequalities, covering linear and nonlinear systems, boundary value problems, and qualitative properties of solutions.

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• Computational Optimal Transport

  now publishers, Inc. eBooks · 2019 · FWCI 52.41 · 909 citations

  This monograph reviews Optimal Transport (OT) with a focus on numerical methods and their data science applications, highlighting recent advancements in approximate solvers that enable scalability for complex problems.

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• Sinc approximation of algebraically decaying functions

  arXiv (Cornell University) · 2018 · 834 citations · Open access

  This paper introduces an extension of sinc interpolation to approximate algebraically decaying functions on the real line.

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• Statistical Aspects of Wasserstein Distances

  Annual Review of Statistics and Its Application · 2018 · Q1 · SJR 3.00 · FWCI 44.93 · 802 citations · Open access

  Wasserstein distances, inspired by optimal mass transportation, offer a versatile statistical tool for measuring differences between probability distributions by incorporating domain geometry and quantifying perturbations.

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• Variational Methods for Nonlocal Fractional Problems

  Cambridge University Press eBooks · 2016 · FWCI 28.63 · 769 citations

  This book offers a comprehensive introduction to the variational analysis of nonlinear problems involving nonlocal operators, presenting both mathematical theory and constructive methods.

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• Elements of Functional Analysis

  2017 · 731 citations

  A summary is not available for this content.

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• Iterative Bregman Projections for Regularized Transportation Problems

  SIAM Journal on Scientific Computing · 2015 · Q1 · SJR 1.00 · FWCI 87.48 · 689 citations

  A new numerical framework uses entropic regularization and iterative Bregman projections to efficiently approximate solutions for optimal transport problems, particularly those with complex constraints.

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• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian

  Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2012 · Q1 · FWCI 35.18 · 676 citations · Open access

  This paper establishes the existence of positive solutions for a specific type of nonlinear Schrödinger equation involving the fractional Laplacian operator.

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• Derivation of transient relativistic fluid dynamics from the Boltzmann equation

  Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology · 2012 · FWCI 41.02 · 642 citations

  A novel method derives transient relativistic fluid dynamics from the Boltzmann equation by retaining all moment expansion terms and identifying microscopic time scales, leading to closure with 14 variables at second order in Knudsen/inverse Reynolds number.

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Recently added

• From fractional Lane–Emden–Serrin equation—existence, multiplicity and local behaviors via classical ODE—to fractional Yamabe metrics with singularity of “maximal” dimension

  Transactions of the American Mathematical Society · 2026 · Q1 · SJR 1.00 · 2 citations · Open access

  A novel first-order ODE is discovered that governs the local behavior of solutions to the fractional Lane–Emden–Serrin equation, allowing for a precise classification up to the second order and linking non-local equations to local ODEs for the first time.

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• A gradient flow for the porous medium equations with Dirichlet boundary conditions

  Journal of Mathematical Analysis and Applications · 2026 · Q1 · 1 citations

  A new gradient flow method constructs weak solutions for porous medium equations with Dirichlet boundary conditions using a modified Wasserstein distance.

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• Principal specialization of monomial symmetric polynomials and group determinants of cyclic groups

  Journal of Algebraic Combinatorics · 2026 · Q1 · 1 citations · Open access

  New explicit formulas for special values of monomial symmetric polynomials at roots of unity are derived, which appear as coefficients in the k-th power of circulant determinants of order n.

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• A General Nonuniqueness Result for Yamabe-Type Problems for Conformally Variational Riemannian Invariants

  Journal of Geometric Analysis · 2026 · Q1 · SJR 1.00 · 1 citations · Open access

  Researchers identified conditions for compact Riemannian manifolds to have many nonhomothetic conformal rescalings with constant scalar invariants, improving nonuniqueness results for Q-curvatures and renormalized volume coefficients.

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• Structural Stability of Prandtl Boundary Layers in the Entire Subsonic Regime

  Archive for Rational Mechanics and Analysis · 2026 · Q1 · SJR 3.00 · FWCI 11.57 · 1 citations · Open access

  The study establishes the structural stability of shear flow boundary layer profiles for 2D steady compressible Navier-Stokes equations across the entire subsonic regime, providing the first rigorous justification for the low Mach number limit with Prandtl-type boundary layers.

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• Well-posedness and singularity formation beyond the Yudovich class

  Journal of the European Mathematical Society · 2026 · Q1 · SJR 3.00 · 1 citations

  Researchers introduce a new class of solutions for the 2D Euler equation that allows for unbounded vorticity, proving local existence and uniqueness and demonstrating that these solutions can develop finite-time singularities, exiting the well-posedness class.

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• Nonlocal Approximation of Minimal Surfaces: Optimal Estimates From Stability

  Communications on Pure and Applied Mathematics · 2026 · Q1 · SJR 4.00 · 1 citations · Open access

  A new nonlocal approximation method for minimal surfaces in 3-manifolds yields optimal estimates for sheet separation and interactions, robust as the approximation parameter approaches zero.

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• Análisis Comparativo y Refutación Determinista de la Incertidumbre Cuántica Óptica de Fluidos en la Variedad RP3 vs. Ortodoxia Probabilística

  Open MIND · 2026 · 2,565 citations

  A new deterministic model of quantum vacuum interactions, based on classical collision mechanics in a viscoelastic medium, accurately predicts solar neutrino detection rates, refuting probabilistic quantum field theories.

  Go to source →

Journals in this field

The journals that publish most of this field’s papers. Quartile (Q1–Q4), SJR and h-index are from SCImago Journal Rank; “in this field” is how many of the journal’s pooled papers belong here. What is a Q1 journal? · What is the h-index?

Every journal in Applied Mathematics (Q1–Q4) →

Other subfields in Mathematics

• Discrete Mathematics and Combinatorics
• Algebra and Number Theory
• Geometry and Topology
• Computational Mathematics
• Statistics and Probability
• Mathematical Physics
• Modeling and Simulation
• Numerical Analysis
• Theoretical Computer Science

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