About
Dr Carlo Mercuri is an Associate Professor of the Mathematics Department at Swansea University.
Dr Carlo Mercuri
Honorary Associate Professor,
Science and Engineering - Faculty
Publications
Research Highlights
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Mercuri, C. & Perera, K. (2022). New multiplicity results for critical p-Laplacian problems. Journal of Functional Analysis, 283(4), 109536
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Dutko, T., Mercuri, C., & Tyler, M. (2021). Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems. Calculus of Variations and Partial Differential Equations, 60(5)
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Bellazzini, J., Ghimenti, M., Mercuri, C., Moroz, V., & Schaftingen, J. (2018). Sharp Gagliardo–Nirenberg inequalities in fractional Coulomb–Sobolev spaces. Transactions of the American Mathematical Society, 370(11), 8285-8310.
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Mercuri, C. & Santos, E. (2019). Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations. Nonlinearity, 32(11), 4445-4464.
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Albalawi, W., Mercuri, C., & Moroz, V. (2020). Groundstate asymptotics for a class of singularly perturbed p-Laplacian problems in $${{\mathbb {R}}}^N$$. Annali di Matematica Pura ed Applicata (1923 -), 199(1), 23-63.
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Farina, A., Mercuri, C., & Willem, M. (2019). A Liouville theorem for the p-Laplacian and related questions. Calculus of Variations and Partial Differential Equations, 58(4)
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Mercuri, C. & Tyler, M. (2020). On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density. Revista Matemática Iberoamericana
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Mercuri, C., Moroz, V., & Schaftingen, J. (2016). Groundstates and radial solutions to nonlinear Schrödinger–Poisson–Slater equations at the critical frequency. Calculus of Variations and Partial Differential Equations, 55(6)
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Mercuri, C., Riey, G., & Sciunzi, B. (2016). A Regularity Result for the p-Laplacian Near Uniform Ellipticity. SIAM Journal on Mathematical Analysis, 48(3), 2059-2075.
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Mercuri, C., Sciunzi, B., & Squassina, M. (2014). On Coron's problem for the p-Laplacian. Journal of Mathematical Analysis and Applications, 421(1), 362-369.
All Research
Journal Articles
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Mercuri, C. & Perera, K. (2022). New multiplicity results for critical p-Laplacian problems. Journal of Functional Analysis, 283(4), 109536
-
Dutko, T., Mercuri, C., & Tyler, M. (2021). Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems. Calculus of Variations and Partial Differential Equations, 60(5)
-
Albalawi, W., Mercuri, C., & Moroz, V. (2020). Groundstate asymptotics for a class of singularly perturbed p-Laplacian problems in $${{\mathbb {R}}}^N$$. Annali di Matematica Pura ed Applicata (1923 -), 199(1), 23-63.
-
Mercuri, C. & Tyler, M. (2020). On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density. Revista Matemática Iberoamericana
-
Mercuri, C. & Santos, E. (2019). Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations. Nonlinearity, 32(11), 4445-4464.
-
Farina, A., Mercuri, C., & Willem, M. (2019). A Liouville theorem for the p-Laplacian and related questions. Calculus of Variations and Partial Differential Equations, 58(4)
-
Bellazzini, J., Ghimenti, M., Mercuri, C., Moroz, V., & Schaftingen, J. (2018). Sharp Gagliardo–Nirenberg inequalities in fractional Coulomb–Sobolev spaces. Transactions of the American Mathematical Society, 370(11), 8285-8310.
-
Mercuri, C., Moroz, V., & Schaftingen, J. (2016). Groundstates and radial solutions to nonlinear Schrödinger–Poisson–Slater equations at the critical frequency. Calculus of Variations and Partial Differential Equations, 55(6)
-
Mercuri, C., Riey, G., & Sciunzi, B. (2016). A Regularity Result for the p-Laplacian Near Uniform Ellipticity. SIAM Journal on Mathematical Analysis, 48(3), 2059-2075.
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Mercuri, C. & Pacella, F. (2014). On the pure critical exponent problem for the $$p$$ -Laplacian. Calculus of Variations and Partial Differential Equations, n/a(n/a), n/a
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Mercuri, C., Sciunzi, B., & Squassina, M. (2014). On Coron's problem for the p-Laplacian. Journal of Mathematical Analysis and Applications, 421(1), 362-369.
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Mercuri, C. & Squassina, M. (2013). Global compactness for a class of quasi-linear elliptic problems. Manuscripta Mathematica, 140(1-2), 119-144.
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BONHEURE, D., DI COSMO, J., & Mercuri, C. (2012). CONCENTRATION ON CIRCLES FOR NONLINEAR SCHRÖDINGER–POISSON SYSTEMS WITH UNBOUNDED POTENTIALS VANISHING AT INFINITY. Communications in Contemporary Mathematics, 14(02), 1250009
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Bonheure, D. & Mercuri, C. (2011). Embedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials. Journal of Differential Equations, 251(4-5), 1056-1085.
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Mercuri, C. & Willem, M. (2010). A global compactness result for the p-Laplacian involving critical nonlinearities. Discrete and Continuous Dynamical Systems, 28(2), 469-493.
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Fall, M. & Mercuri, C. (2009). Foliations of small tubes in Riemannian manifolds by capillary minimal discs. Nonlinear Analysis: Theory, Methods & Applications, 70(12), 4422-4440.
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Fall, M. & Mercuri, C. (2009). Minimal disc-type surfaces embedded in a perturbed cylinder. Differential and Integral Equations, 22(11/12), 1115-1124.SU Repository: https://cronfa.swan.ac.uk/Record/cronfa30803
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Mercuri, C. (2008). Positive solutions of nonlinear Schrödinger–Poisson systems with radial potentials vanishing at infinity. Rendiconti Lincei - Matematica e Applicazioni, 211-227.
Supervision
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Solutions to a class of nonlinear Schrödinger equations involving a nonlocal term. (current)
PhDOther supervisor: Prof Michael EdwardsOther supervisor: Dr Dmitri Finkelshtein -
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion (awarded 2022)
PhDOther supervisor: Prof Elaine Crooks
Taught Modules
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MA-241 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.
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MA-360 Dissertation in Mathematics and Computer Science
This module provides the opportunity to explore a topic within Mathematics and Computer Science and independently learn new subjects with the guidance of a member of staff.