Dr Carlo Mercuri
Senior Lecturer
Mathematics
Telephone: (01792) 602762
Room: Office - 204
Second Floor
Talbot Building
Singleton Campus

Areas of Expertise

  • Nonlinear Analysis
  • Partial Differential Equations
  • Critical Point Theory
  • Variational Methods

Publications

  1. & Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces. Transactions of the American Mathematical Society, 1
  2. & Groundstates and radial solutions to nonlinear Schrödinger–Poisson–Slater equations at the critical frequency. Calculus of Variations and Partial Differential Equations 55(6)
  3. & A Regularity Result for the p-Laplacian Near Uniform Ellipticity. SIAM Journal on Mathematical Analysis 48(3), 2059-2075.
  4. & On Coron's problem for the p-Laplacian. Journal of Mathematical Analysis and Applications 421(1), 362-369.
  5. & On the pure critical exponent problem for the $$p$$ -Laplacian. Calculus of Variations and Partial Differential Equations n/a(n/a), n/a

See more...

Teaching

  • MA-241 Introduction to Ordinary Differential Equations

    This module is an elementary course on the theory and methods for ordinary differential equations (ODEs). It combines a rigorous approach to the existence and uniqueness of solutions with methods for finding explicit solutions to ODEs. Applications are discussed to concrete problems in Physics and Biology.

  • MA-314 Differential Equations

    This module is an advanced course on the theory and methods for ordinary differential equations. It combines questions about the existence, uniqueness and properties of solutions to ODEs with methods of finding the explicit solutions to linear ODEs. Applications of ODEs methods to some classes of initial boundary value problems for partial differential equations are also discussed.

  • MA-M14 Differential Equations

    This module is an advanced course on the theory and methods for ordinary differential equations. It combines questions about the existence, uniqueness and properties of solutions to ODEs with methods of finding the explicit solutions to linear ODEs. Applications of ODEs methods to some classes of initial boundary value problems for partial differential equations are also discussed.

Supervision

  • Existence and Qualitative Properties of Solutions to Non Linear Schodinger-Poisson Systems (current)

    Student name:
    PhD
    Other supervisor: Dr Elaine Crooks
  • Some Nonlinear Problems With Lack Of Compactness (current)

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

    Student name:
    PhD
    Other supervisor: Prof Vitaly Moroz