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. Defence 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. Defence date: March 26, 2020.
  3. Ph.D. Dissertation, Friedrich-Alexander-Universität Erlangen-Nürnberg, supervised by Enrique Zuazua. Work in progress. Defence date: tbd (2023).

Papers

  1. Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation, together with Julian Fischer. To appear in Communications in Partial Differential Equations (2022). Preprint link.
  2. Differentiability in measure of the flow associated with a nearly incompressible BV vector field, together with Stefano Bianchini. In revision at Archive for Rational Mechanics and Analysis (2021). Preprint 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(3): 957-985 (2021). Preprint link. Journal link (Special Issue dedicated to Enrique Zuazua on the occasion of his 60th birthday).
  4. Singular limits with vanishing viscosity for nonlocal conservation laws, together with Giuseppe Maria Coclite, Alexander Keimer, and Lukas Pflug. Nonlinear Analysis, 211 (2021). Preprint 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. To appear in Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire (2021). Preprint 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(3): 413-426 (2021). Preprint 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. To appear in Zeitschrift für Angewandte Mathematik und Physik (2022). Preprint link.
  8. On Liouville-type theorems for the 2D stationary MHD equations, together with Francis Hounkpe and Simon Schulz. Nonlinearity, 35(2): 870-888 (2022). Preprint 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. Critical functions and blow-up asymptotics for the fractional Brezis–Nirenberg problem in low dimension, together with Tobias König. Submitted (2021). Preprint link.
  11. On the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methods, together with Enrique Zuazua. Submitted (2021). Preprint link.
  12. The stationary critical points of the fractional heat flow, together with Shigeru Sakaguchi. Submitted (2022). Preprint link.