Professor
Mathematics
Telephone: (01792) 602763
Room: Office - 306
Third Floor
Computational Foundry
Bay Campus

My research interest is in the theory of nonlinear partial differential equations. It is focussed on the fundamental questions of existence, non-existence, and structure of solution sets of nonlinear elliptic equations and inequalities. My recent research concentrates in the area known in the modern PDE literature as nonlinear Liouville type theorems. I am also interested in concentarion phenomena in nonlinear PDEs. Most recently I was working on nonlinear elliptic problems with nonlocal interactions, such as Choquard (or Schrödinger-Newton) type equations.
My earlier research was in the area of topological and variational methods of nonlinear analysis, in particular critical points theory, infinite dimensional Morse Theory and its applications to nonlinear elliptic equations and nonlinear problems associated with non-local operators.

Areas of Expertise

  • Nonlinear partial differential equations

Publications

  1. & Groundstate asymptotics for a class of singularly perturbed p-Laplacian problems in RN. Annali di Matematica Pura ed Applicata (1923 -), 1-41.
  2. & Sharp Gagliardo–Nirenberg inequalities in fractional Coulomb–Sobolev spaces. Transactions of the American Mathematical Society 370(11), 8285-8310.
  3. & Moderate solutions of semilinear elliptic equations with Hardy potential under minimal restrictions on the potential. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 18(1), 39-64.
  4. & Boundary singularities of solutions of semilinear elliptic equations in the half-space with a Hardy potential. Israel Journal of Mathematics 222(1), 487-514.
  5. & A guide to the Choquard equation. Journal of Fixed Point Theory and Applications 19(1), 773-813.

See more...

Teaching

  • MA-201 Real Analysis and Metric Spaces

    The module extends ideas such as continuity and convergence to metric spaces introducing completeness and compactness and consequential results.

  • MA-311 Partial Differential Equations

    This course provides an introduction to the theory of partial differential equations form an analytical perspective.

  • MA-M11 Partial Differential Equations

    This course provides an introduction to the theory of partial differential equations form an analytical perspective.

  • MAW201 Dadansoddi Real a Gofodau Metrig

    Mae'r modiwl hwn yn estyn syniadau fel didoriant a chydgyfeiriant i wagleoedd metrig gan gyflwyno cyflawnrwydd a chrynoder a chanlyniadau ol-ddilynol.

Supervision

  • Untitled (current)

    Student name:
    PhD
    Other supervisor: Prof Elaine Crooks
  • Mathematical analysis of Thomas-Fermi theory for graphene (current)

    Student name:
    MPhil
    Other supervisor: Prof Elaine Crooks
  • Chemical potential for Bose-Einstein condensate in infinitie volume by GPE model (awarded 2018)

    Student name:
    PhD
    Other supervisor: Dr Zeev Sobol
  • '''Asymptotic behaviour of the ground state of quasilinear elliptic equation with a vanishing parameter''' (awarded 2017)

    Student name:
    PhD
    Other supervisor: Dr Carlo Mercuri

Administrative Responsibilities

  • Deputy Programme Director - Department of Mathematics

    2012 - Present

External Responsibilities