Fields · Physical Sciences · Mathematics · Applied Mathematics

Nonlinear Partial Differential Equations

This cluster of papers focuses on the theory of fractional Laplacian operators, including topics such as Sobolev spaces, nonlinear equations, regularity theory, variational problems, critical exponents, ground state solutions, elliptic equations, nonlocal operators, and Hamiltonian estimates.

62,145 works

Papers listed on taxonomy pages are the top few works per node from the OpenAlex snapshot. That list is not exhaustive and is not an endorsement. The topic map and the journal registry remain separate: there is still no authoritative topic-to-venue or topic-to-organization edge. Search is a lexical lookup, not a claim that a venue publishes a topic.

Most cited

  1. Hitchhikerʼs guide to the fractional Sobolev spaces

    Eleonora Di Nezza, Giampiero Palatucci, Enrico Valdinoci · 2011 · Bulletin des Sciences Mathématiques · 4,335 citations

  2. Symmetry and related properties via the maximum principle

    Basilis Gidas, Wei‐Ming Ni, Louis Nirenberg · 1979 · Communications in Mathematical Physics · 2,926 citations

  3. Positive solutions of nonlinear elliptic equations involving critical sobolev exponents

    Haïm Brézis, Louis Nirenberg · 1983 · Communications on Pure and Applied Mathematics · 2,921 citations

  4. An Extension Problem Related to the Fractional Laplacian

    Luis Caffarelli, Luis Silvestre · 2007 · Communications in Partial Differential Equations · 2,327 citations

  5. Best constant in Sobolev inequality

    Giorgio Talenti · 1976 · Annali di Matematica Pura ed Applicata (1923 -) · 2,201 citations

  6. Logarithmic Sobolev Inequalities

    Leonard Gross · 1975 · American Journal of Mathematics · 1,852 citations

Most recent

  1. Serrin’s overdetermined problems on epigraphs

    Nicolas Beuvin, Alberto Farina · 2026 · Mathematische Annalen · 0 citations

  2. On the defocusing stationary nonlinear Schrödinger equation on metric graphs

    Élio Durand-Simonnet, Damien Galant, Boris Shakarov · 2026 · Journal of Differential Equations · 0 citations

  3. Second boundary value problems for Hessian curvature equations

    Rongli Huang, Changzheng Qu, Zhizhang Wang, Weifeng Wo · 2026 · Mathematische Annalen · 0 citations

  4. On finite-energy solutions of Kazdan-Warner type equations on the lattice graph

    Huyuan Chen, Bobo Hua · 2026 · Communications in Partial Differential Equations · 0 citations

  5. Multiple Normalized Solutions for p-Laplacian Schrödinger–Poisson Systems

    Mengru Li, Xiaoming He, Marco Squassina · 2026 · Asymptotic Analysis · 0 citations

  6. Normalized solutions for magnetic p-Laplacian equations coupled with nonlocal Poisson potentials and critical nonlinearities

    Khaled Khachnaoui · 2026 · Quaestiones Mathematicae · 0 citations

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