Dr Antonio Esposito

PhD, MSc, BSc

Status

Postdoctoral Research Associate

+44 1865 615129

Contact form

https://sites.google.com/view/antonioespositomath

ORCID iD

https://orcid.org/0000-0002-4230-4729

Research groups

Oxford Centre for Nonlinear PDE

Address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Major / recent publications

Well-posedness of an integro-differential model for active Brownian particles,
Bruna, M Burger, M Esposito, A Schulz, S
SIAM Journal on Mathematical Analysis, 54, (2022), no. 5, 5662 - 5697
https://doi.org/10.1137/21M1462039 - arXiv:2111.13245.

Many-particle limit for a system of interaction equations driven by Newtonian potentials
Di Francesco, M Esposito, A Schmidtchen, M
Calculus of Variations and Partial Differential Equations (2021)
https://doi.org/10.1007/s00526-021-01960-

Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit
Esposito, A Patacchini, F S Schlichting, A Slepčev, D
Archive for Rational Mechanics and Analysis (2021)
https://doi.org/10.1007/s00205-021-01631-w

Nonlinear degenerate cross-diffusion systems with nonlocal interaction
Di Francesco, M Esposito, A Fagioli, S
Nonlinear Analysis, vol. 169, pp. 94-117 (2018)
https://doi.org/10.1016/j.na.2017.12.003

Research interests

My research focuses on the analysis of partial differential equations (PDEs) modelling nonlocal interaction and/or aggregation-diffusion phenomena. The study of these PDEs arises from applications in, among others, social sciences, biology and data science. More precisely I am interested in gradient flows and their generalisation, including applications to kinetic theory and data science, optimal transport theory applied to evolutionary PDEs, systems of PDEs with nonlinear cross-diffusion and nonlocal interactions, PDEs on graphs/networks, particle approximation for (systems of ) nonlocal PDEs.

Recent publications

Nonlocal particle approximation for linear and fast diffusion equations

Carrillo, J Esposito, A Skrzeczkowski, J Wu, J (05 Aug 2024) http://arxiv.org/abs/2408.02345v1

Competing effects in fourth‐order aggregation–diffusion equations

Antonio Carrillo, J Esposito, A Falcó, C Fernández‐Jiménez, A Proceedings of the London Mathematical Society volume 129 issue 2 (22 Jul 2024)

On a novel gradient flow structure for the aggregation equation

Esposito, A Gvalani, R Schlichting, A Schmidtchen, M Calculus of Variations and Partial Differential Equations volume 63 issue 5 (05 May 2024)

Nonlocal approximation of nonlinear diffusion equations

Carrillo, J Esposito, A Wu, J Calculus of Variations and Partial Differential Equations (16 Feb 2023)

On evolution PDEs on co-evolving graphs

Esposito, A Mikolás, L Discrete and Continuous Dynamical Systems - Series A volume 44 issue 9 2660-2683 (02 Apr 2024)

On evolution PDEs on co-evolving graphs

Esposito, A Mikolás, L (16 Oct 2023)

Prizes, awards, and scholarships

Grant for Research in Paris at the Institute Henri Poincarè, Paris, March, 2020.

Fellowship to participate to the Junior Trimester Program ''Kinetic Theory'' at the Hausdorff Research Institute for Mathematics, Bonn, Germany, May-August, 2019.

Grant awarded by the French Embassy in Italy for the organisation of study days to foster collaborations with researchers from French institutions - Grant used to co-organise a mini-workshop at the Gran Sasso Science Instutite in April 2017.