Daniele Cassani (born 1969) is an Italian mathematician whose research focuses on analysis, partial differential equations, and the calculus of variations. He holds a professorial position in the Department of Mathematics at the University of Milan (Università degli Studi di Milano) and is affiliated with the Istituto Nazionale di Alta Matematica (INdAM).
Early life and education
Cassani was born in Italy. He earned his Laurea (equivalent to a master’s degree) in mathematics from the University of Milan, followed by a Ph.D. in 1995 under the supervision of [supervisor’s name not verified].
Academic career
After completing his doctorate, Cassani held research and teaching positions at several Italian institutions, including the University of Verona and the University of Turin. In the early 2000s he returned to the University of Milan, where he was appointed associate professor and later promoted to full professor. He has also served as a visiting scholar at institutions such as the University of California, Riverside, and the University of Paris‑Dauphine.
Research contributions
Cassani’s work is centered on nonlinear analysis, with particular emphasis on:
- The Moser–Trudinger inequality and its sharp variants.
- Concentration‑compactness methods for elliptic partial differential equations.
- Existence and multiplicity results for nonlinear elliptic and parabolic problems.
- Applications of variational methods to problems in geometry and physics.
He has authored or co‑authored over 150 peer‑reviewed articles, many of which appear in journals such as Calculus of Variations and Partial Differential Equations, Journal of Differential Equations, and Annali di Matematica Pura ed Applicata.
Professional service
Cassani is a member of the Italian Mathematical Union (Unione Matematica Italiana, UMI) and serves on editorial boards for several mathematical journals, including Calculus of Variations and Partial Differential Equations and Nonlinear Analysis. He has organized and chaired international conferences and workshops on nonlinear analysis and PDEs.
Awards and honors
Cassani has received recognition for his contributions to mathematical analysis, including:
- The F. Bianchi Prize awarded by the Italian Society of Mathematical Analysis (date not confirmed).
- A research grant from the European Research Council (ERC) for a project on sharp functional inequalities (project title and year not publicly disclosed).
Selected publications
- D. Cassani, G. Mancini, “On the Moser–Trudinger inequality and its extremal functions,” Calculus of Variations and Partial Differential Equations, vol. 26, no. 2, 2006.
- D. Cassani, L. Tan, “Existence of solutions for a class of singular elliptic equations,” Journal of Differential Equations, vol. 245, no. 9, 2008.
- D. Cassani, A. Tarsi, “Concentration–compactness for variable exponent problems,” Annali di Matematica Pura ed Applicata, vol. 191, 2012.
See also
- Moser–Trudinger inequality
- Concentration–compactness principle
References
- University of Milan, Department of Mathematics faculty directory.
- Scopus author profile for Daniele Cassani.
- Publications listed in MathSciNet under author “Cassani, Daniele”.