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Nicola Garofalo

Nicola Garofalo

D-Index & Metrics

Mathematics

D-Index
46
Citations
7699
World Ranking
1373
National Ranking
36

Overview

Nicola Garofalo is affiliated with the University of Padua in Italy and specializes mainly in the field of Mathematics. Their research emphasizes applied mathematics, mathematical physics, and computational theory, with additional interests extending to astronomy and astrophysics as well as genetics.

The primary topics addressed in Garofalo's body of work include:

  • Nonlinear Partial Differential Equations
  • Advanced Mathematical Modeling in Engineering
  • Numerical Methods in Inverse Problems
  • Geometric Analysis and Curvature Flows
  • Differential Equations and Boundary Problems
  • Advanced Harmonic Analysis Research
  • Advanced Mathematical Physics Problems

Garofalo's research output is heavily represented in several key publication venues, including:

  • arXiv (Cornell University)
  • Institutional Research Information System University of Ferrara (University of Ferrara)
  • Padua Research Archive (University of Padua)
  • Journal of Functional Analysis
  • Proceedings of the American Mathematical Society

Recent papers published by Nicola Garofalo feature investigations into aspects of partial differential equations and hypoelliptic semigroups. Notable recent publications are:

  • "Nonlocal isoperimetric inequalities for Kolmogorov-Fokker-Planck operators" (2020), Institutional Research Information System University of Ferrara (University of Ferrara)
  • "Hardy-Littlewood-Sobolev inequalities for a class of non-symmetric and non-doubling hypoelliptic semigroups" (2022), Institutional Research Information System University of Ferrara (University of Ferrara)
  • "Feeling the heat in a group of Heisenberg type" (2021), Advances in Mathematics
  • "A Bourgain-Brezis-Mironescu-Dávila theorem in Carnot groups of step two" (2023), Communications in Analysis and Geometry
  • "Heat Kernels for a Class of Hybrid Evolution Equations" (2022), Potential Analysis

Collaboration is a significant element in Garofalo's research career, with frequent co-authors including:

  • Agnid Banerjee
  • Giulio Tralli
  • Federico Buseghin
  • Ramesh Manna
  • Donatella Danielli

Overall, Garofalo's scientific contributions lie in advancing the understanding of mathematical structures in applied mathematics and physics through analytical techniques, computational approaches, and theoretical exploration.

Best Publications

  • Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces

    Nicola Garofalo;Duy Minh Nhieu

  • Unique continuation for elliptic operators: A geometric‐variational approach

    Nicola Garofalo;Fang‐Hua ‐H Lin

  • Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation

    Nicola Garofalo;Ermanno Lanconelli

  • An embedding theorem and the harnack inequality for nonlinear subelliptic equations

    Luca Capogna;Donatella Danielli;Nicola Garofalo

  • Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries

    Fabrice Baudoin;Nicola Garofalo

  • The geometric Sobolev embedding for vector fields and the isoperimetric inequality

    Luca Capogna;Donatella Danielli;Nicola Garofalo

  • Existence and nonexistence results for semilinear equations on the Heisenberg group

    N. Garofalo;E. Lanconelli

  • Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces

    Nicola Garofalo;Duy Minh Nhieu

  • Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem

    Nicola Garofalo;Arshak Petrosyan

  • A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations

    Eugene B. Fabes;Nicola Garofalo;Sandro Salsa

  • HARNACK'S INEQUALITY FOR SUM OF SQUARES OF VECTOR FIELDS PLUS A POTENTIAL

    Giovanna Citti;Nicola Garofalo;Ermanno Lanconelli

  • A gradient bound for entire solutions of quasi‐linear equations and its consequences

    Luis Caffarelli;Nicola Garofalo;Fausto Segala

  • CAPACITARY ESTIMATES AND THE LOCAL BEHAVIOR OF SOLUTIONS OF NONLINEAR SUBELLIPTIC EQUATIONS

    Luca Capogna;Donatella Danielli;Nicola Garofalo

  • Notions of Convexity in Carnot Groups

    Donatella Danielli;Nicola Garofalo;Nicola Garofalo;Duy Minh Nhieu

  • Harnack’s inequality for Schrödinger operators and the continuity of solutions

    F. Chiarenza;E. Fabes;N. Garofalo

  • Sub-Riemannian calculus on hypersurfaces in Carnot groups

    Donatella Danielli;Nicola Garofalo;Duy-Minh Nhieu

  • A symmetry result related to some overdetermined boundary value problems

    Nicola Garofalo;John L. Lewis

  • Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type

    Nicola Garofalo;Dimiter Vassilev

  • Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups

    Nicola Garofalo;Dimiter Vassilev

  • Trace inequalities for Carnot-Carathéodory spaces and applications

    Donatella Danielli;Nicola Garofalo;Duy-Minh Nhieu

Frequent Co-Authors

Eugene B. Fabes
Eugene B. Fabes University of Minnesota
Fanghua Lin
Fanghua Lin Courant Institute of Mathematical Sciences
Luis A. Caffarelli
Luis A. Caffarelli The University of Texas at Austin
Michael Ruzhansky
Michael Ruzhansky Ghent University
Giovanni Alessandrini
Giovanni Alessandrini University of Trieste

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