Publications

“The product of mathematics is clarity and understanding. Not theorems, by themselves.”

—William P. Thurston, What’s a mathematician to do?, 2010.

“Peer’s law. The solution to a problem changes the nature of the problem.”

—Arthur Bloch, Murphy’s Law: Complete, Arrow Books, 2002, p. 54.

“La dernière chose c’est la simplicité. Après avoir épuisé toutes les difficultés, après avoir joué une immense quantité de notes, et de notes, c’est la simplicité qui sort avec tout son charme, comme le dernier sceau de l’art.”

—Frederick Nicks, Frederick Chopin as a Man and Musician, Novello and Co., vol. II, Appendix IX, p. 596.

Theses

  1. Well-posedness of viscosity solutions for a class of integro-differential equations modeling pricing under uncertainty. Tesi di Laurea, Università degli Studi di Bari Aldo Moro, supervised by Giuseppe Maria Coclite and Mario Michele Coclite. Defense date: March 16, 2018.
  2. Differentiability properties of the flow associated to a rough vector field. Tesi di Laurea Magistrale, Università degli Studi di Bari Aldo Moro, supervised by Stefano Bianchini, Giuseppe Maria Coclite, and Luciano Lopez. Defense date: March 26, 2020.
  3. Analysis, control, and singular limits for hyperbolic conservation laws. Ph.D. Dissertation, Friedrich-Alexander-Universität Erlangen-Nürnberg, supervised by Enrique Zuazua. Work in progress. Defense date: tbd (expected in the Summer Semester 2023).

Papers

  1. Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation, together with Julian Fischer. Communications in Partial Differential Equations 47, No. 7, 1394–1434 (2022). Reprint link. Journal link.
  2. Differentiability in measure of the flow associated with a nearly incompressible BV vector field, together with Stefano Bianchini. Archive for Rational Mechanics and Analysis 246, No. 2-3, 659–734 (2022). Reprint link. Journal link.
  3. Boundary controllability and asymptotic stabilization of a nonlocal traffic flow model, together with Alexandre Bayen, Jean-Michel Coron, Alexander Keimer, and Lukas Pflug. Vietnam Journal of Mathematics 49, No. 3, 957–985 (2021). Reprint link. Journal link.
  4. Singular limits with vanishing viscosity for nonlocal conservation laws, together with Giuseppe Maria Coclite, Alexander Keimer, and Lukas Pflug. Nonlinear Analysis 211, Article ID 112370, 12 p. (2021). Reprint link. Journal link.
  5. A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels, together with Giuseppe Maria Coclite, Jean-Michel Coron, Alexander Keimer, and Lukas Pflug. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire (2022). Reprint link. Journal link.
  6. Vanishing viscosity for a 2 × 2 system modeling congested vehicular traffic, together with Giuseppe Maria Coclite, Mauro Garavello, and Francesca Marcellini. Networks & Heterogeneous Media 16, No. 3, 413–426 (2021). Reprint link. Journal link.
  7. On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels, together with Giuseppe Maria Coclite, Alexander Keimer, and Lukas Pflug. Zeitschrift für Angewandte Mathematik und Physik 73, No. 6, Paper No. 241, 10 p. (2022). Reprint link. Journal link.
  8. On Liouville-type theorems for the 2D stationary MHD equations, together with Francis Hounkpe and Simon Schulz. Nonlinearity 35, No. 2, 870–888 (2022). Reprint link. Journal link.
  9. Control of hyperbolic and parabolic equations on networks and singular limits, together with Jon Asier Barcena-Petisco, Marcio Cavalcante, Giuseppe Maria Coclite, and Enrique Zuazua. Submitted (2021). Preprint link.
  10. On the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methods, together with Enrique Zuazua. Vietnam Journal of Mathematics 51, 71–88 (2023). Reprint link. Journal link.
  11. Critical functions and blow-up asymptotics for the fractional Brezis–Nirenberg problem in low dimension, together with Tobias König. Calculus of Variations and Partial Differential Equations 62, Paper No. 114 (2023). Preprint link. Journal link.
  12. The stationary critical points of the fractional heat flow, together with Shigeru Sakaguchi. Submitted (2022). Preprint link.
  13. On the decay of one-dimensional locally and partially dissipated hyperbolic systems, together with Timothée Crin-Barat and Enrique Zuazua. Submitted (2022). Preprint link.
  14. Interface propagation properties for a fractional thin-film equation, together with Roman Taranets. Submitted (2022). Preprint link.
  15. Stability with explicit constants of the critical points of the fractional Sobolev inequality and applications to fast diffusion, together with Tobias König. Submitted (2022). Preprint link.
  16. Fractional Hardy-Rellich inequalities via a Pohozaev identity, together with Sidy Moctar Djitte. Submitted (2023). Preprint link.
  17. Scaling limits for fractional polyharmonic Gaussian fields, together with Florian Schweiger. Submitted (2023). Preprint link.
  18. Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave, together with Giuseppe Maria Coclite, Alexander Keimer, Lukas Pflug, and Enrique Zuazua. Submitted (2023). Preprint link.
  19. Oleĭnik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit, together with Giuseppe Maria Coclite, Maria Colombo, Gianluca Crippa, Alexander Keimer, Elio Marconi, Lukas Pflug, and Laura Valentina Spinolo. Submitted (2023). Preprint link.
  20. Symmetry results for some overdetermined obstacle problems, together with Shigeru Sakaguchi. Submitted (2023). Preprint link.