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:

• PDEs on graphs/networks.

• Particle approximation for (systems of ) PDEs.

• Optimal transport theory applied to evolutionary PDEs: gradient flows and their generalisation.

• Systems of PDEs with nonlinear cross-diffusion and nonlocal interactions.

• Parabolic and Hyperbolic PDEs.

Preprints

1. A. Esposito, G. Heinze, A. Schlichting, Graph-to-local limit for the nonlocal interaction equation, preprint arXiv:2306.03475.

Publications

1. J. A. Carrillo, A. Esposito, C. Falcó, A. Fernández-Jiménez, Competing effects in fourth-order aggregation-diffusion equations, to appear in Proceedings of the London Mathematical Society, preprint arXiv:2307.14706.

2. A. Esposito, L. Mikolás, On evolution PDEs on co-evolving graphs, Discrete & Continuous Dynamical Systems - A, 2024, 44(9): 2660-2683 - https://doi.org/10.3934/dcds.2024041 - arXiv:2310.10350.

3. J. A. Carrillo, A. Esposito, J. S.-H. Wu, Nonlocal approximation of nonlinear diffusion equations, Calculus of Variations and Partial Differential Equations, 63, 100 (2024) https://doi.org/10.1007/s00526-024-02690-z - arXiv:2302.08248.

4. A. Esposito, R. S. Gvalani, A. Schlichting, M. Schmidtchen, On a novel gradient flow structure for the aggregation equation, Calculus of Variations and Partial Differential Equations, 63, 126 (2024) https://doi.org/10.1007/s00526-024-02692-x - arXiv:2112.08317.

5. M. Burger, A. Esposito, Porous medium equation and cross-diffusion systems as limit of nonlocal interaction, Nonlinear Analysis, 235, 113347 (2023) - https://doi.org/10.1016/j.na.2023.113347 -  arXiv:2202.05030.

6. A. Esposito, F. S. Patacchini, A. Schlichting, On a Class of Nonlocal Continuity Equations on Graphs, European Journal of Applied Mathematics, 1-18 (2023) - https://doi.org/10.1017/S0956792523000128 - arXiv:2209.15552.

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

8. M. Bruna, M. Burger, A. Esposito, S. Schulz, Phase Separation in Systems of Interacting Active Brownian Particles, SIAM Journal on Applied Mathematics, 82 (2022), no. 4, 1635–1660 - https://doi.org/10.1137/21M1452524 - arXiv:2110.07054.

9. M. Di Francesco, A. Esposito, M. Schmidtchen, Many-particle limit for a system of interaction equations driven by Newtonian potentials, Calculus of Variations and Partial Differential Equations 60, 68 (2021) - https://doi.org/10.1007/s00526-021-01960-4 - arXiv:2008.11106.

10. A. Esposito, F. S. Patacchini, A. Schlichting, D. Slepčev, Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit, Archive for Rational Mechanics and Analysis (2021) - https://doi.org/10.1007/s00205-021-01631-w - arXiv:1912.09834

11. J. A. Carrillo, M. Di Francesco, A. Esposito, S. Fagioli, M. Schmidtchen, Measure solutions to a system of continuity equations driven by Newtonian nonlocal interactions, Discrete & Continuous Dynamical Systems - A, vol. 40, no. 2, pp. 1191–1231 (2020) -http://dx.doi.org/10.3934/dcds.2020075 - preprint version

12. A. Esposito, F. Leonetti, P.V. Petricca, Absence of Lavrentiev gap for nonautonomous functionals with (p,q)-growth, Advances in Nonlinear Analysis, vol. 8, pp. 73-78 (2019) - https://doi.org/10.1515/anona-2016-0198

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

14. A. Esposito, T. Radice, R. Schiattarella, Duality for borderline Ap-weights and Gq-weights on R, Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche, vol. 82; pp. 107-114 (2015)

Proceedings

1. A. Esposito, G. Heinze, J.-F. Pietschmann, A. Schlichting, Graph-to-local limit for a multi-species nonlocal cross-interaction system, Proceedings in Applied Mathematics & Mechanics (2023) - https://doi.org/10.1002/pamm.202300094 - preprint version