CASSANI DANIELE

Sito web:

http://www.uninsubria.it/hpp/daniele.cassani

Email

Phone

0332 21 8771,0332 21 8772

Biographic note

Daniele Cassani obtained his masters' degree with summa cum laude in pure Mathematics in 2001 and the PhD in pure Mathematics in 2006 at Università degli Studi di Milano, under the guidance of B. Ruf. Right after that he spent one year as visiting post-doc at Pacific Institute for Mathematical Sciences, University of British Columbia (Vancouver), directed by I. Ekeland and under the supervision of N. Ghoussoub. Since 2007 to 2011 he obtained a postdoc position at Università di Milano and as Lecturer at Politecnico di Milano. In 2012 senior research fellow at Dep. of Science and High Technology, Università degli Studi dell'Insubria, since 2017 Associate Professor and since 2023 Full Professor of Mathematical Analysis. He has been invited as visiting professor and speakers at international conferences by prestigious institutions in Europe, China, North and South America, Japan. He works as reviewer for several international recognized journals and since 2019 as Springer associate editor for the Milan Journal of Mathematics. Since 2016 president of the Riemann International School of Mathematics. From 2018 to 2023 member of the Board of Directors of the university and form 2021 to 2023 PI for the establishment of the Foundation University of Insubria. Since 2023 CEO of the Foundation University of Insubria.

His research interests focus on Nonlinear Analysis and Calculus of Variations, Partial Differential Equations and Inequalities, Systems of PDE and Applications to MEMS. Solitons Field Theory, Best constants in functional inequalities, Maximum principle, Inverse problems, Image processing.

Research

Publications

1. D. Cassani, Existence and non-existence of solitary waves for the critical Klein-Gordon equation coupled with Maxwell's equations, Nonlinear Analysis 58 (2004), 733-747. 2. D. Cassani, Nonlinear elliptic systems with critical growth, Università degli Studi di Milano, Tesi di Dottorato di Ricerca (2005), Lambert Academic Publishing (2010), 70pp. 3. D. Cassani, Remarks on a `Serrin curve' for systems of differential inequalities, Rend. Cl. Sci. Mat. Nat. 140 (2006), 115-126 (2009). 4. D. Cassani, J.M. do O and N. Ghoussoub, On a fourth order elliptic problem with a singular nonlinearity, Adv. Nonlinear Stud. 9 (2009), 189-209. 5. D. Cassani, J.M. do O and A. Moameni, Existence and concentration of solitary waves for a class of quasilinear Schrodinger equations, Commun. Pure Appl. Anal. 9 (2010), 281-306. 6. D. Cassani and C. Tarsi, A Moser-type inequality in Lorentz-Sobolev spaces for unbounded domains in R^N, Asymptotic Analysis 64 (2009), 29-51. 7. D. Cassani, Lorentz-Sobolev spaces and systems of Schrodinger equations in R^N, Nonlinear Analysis 70 (2009), 2846-2854. 8. E. Berchio, D. Cassani and F. Gazzola, Hardy-Rellich inequalities with boundary remainder terms and applications, Manuscripta Mathematica 131 (2010), 427-458. 9. D. Cassani, B. Kaltenbacher and A. Lorenzi, Direct and inverse problems related to MEMS, Inverse Problems 25 (2009), 105002 (22pp). 10. D. Cassani, B. Ruf and C. Tarsi, Best constants in a borderline case of second order Moser type inequalities, Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010), 73-93. 11. D. Cassani, B. Ruf and C. Tarsi, Best constants for Moser type inequalities in Zygmund spaces, Matematica Contemporanea 36 (2009), 79-90. 12. D. Cassani, L. Fattorusso and A. Tarsia, Global existence for nonlocal MEMS, Nonlinear Analysis 74 (2011), 5722-5726. 13. D. Cassani, B. Ruf and C. Tarsi, Group invariance and Pohozaev identities in Moser type inequalities, Comm. Contemp. Math., 15 (2013), 1250054 (20pp) 14. D. Cassani, B. Ruf and C. Tarsi, Optimal Sobolev-type inequalities in Lorentz spaces, Potential Analysis 39 (2013), 265-285. 15. D. Cassani, B. Ruf and C. Tarsi, A Moser type inequality in Zygmund spaces without boundary conditions, Contemporary Mathematics 595 (2013), Recent Trends in Nonlinear Partial Differential Equations II: Stationary Problems, (22pp). 16. D. Cassani, L.Fattorusso and A.Tarsia, Nonlocal dynamic problems with singular nonlinearities and applications to MEMS, Progress in Nonlinear Differential Equations and their Applications, Birkhauser 2014, (22pp). 17. Z.-J. Bai, D. Cassani, M. Donatelli and S. Serra Capizzano, A Fast Alternating Minimization Algorithm for Total Variation Deblurring Without Boundary Artifacts, Journal of Mathematical Analysis and Applications, 415 (2014), 373-393. 18. D. Cassani, F. Sani and C. Tarsi, Equivalent Moser type inequalities in R2 and the zero mass case, Journal of Functional Analysis 267 (2014), 4236-4263. 19. D. Cassani and C.Tarsi, Existence of solitary waves for supercritical Schroedinger systems in dimension two, Calculus of Variations and PDE 54 (2015), 1673-1704. 20. D. Cassani and A.Tarsia, Periodic solutions to nonocal MEMS equations, Discrete Contin. Dyn. Syst. Ser. S. 9 (2016), 631-642. 21. C. Alves, D. Cassani, C. Tarsi and M. Yang, Existence and concentration of ground state solutions for a critical nonlocal Schroedinger equation in R2, Journal of Differential Equations 261 (2016), 1933-1972. 22. D. Cassani, J.M. do O' and J. Zhang, Multi-pump solutions for singularly perturbed Schroedinger equations in R2 with general nonlinearities, Topological Methods in Nonlinear Analysis 49 (2017), 205-231. 23. D. Cassani and J. Zhang, A priori estimates and positivity for semiclassical ground states for systems of critical Schroedinger equations in dimension two, Communications in Partial Differential Equations 42 (2017), 655-702. 24. D. Cassani, B. Ruf and C. Tarsi, Equivalent and attained version of Hardy’s inequality in Rn, J. Funct. Anal. 275 (2018), 3303–3324. 25. D. Cassani, B. Ruf and C. Tarsi, On the capacity approach to non-attainability of Hardy’s inequality in Rn, Discrete Contin. Dyn. Syst. Ser. S. 12 (2019), 245–250. 26. D. Cassani and J. Zhang, Choquard type equations with Hardy-Littlewood-Sobolev upper-critical growth, Adv. NonlinearAnal. 8 (2019), 1184–1212. 27. D. Cassani, Z. Liu, C. Tarsi and J. Zhang, Multiplicity of sign-changing solutions for Kirchhoff type equations, Nonlinear Anal. 186 (2019), 145–161. 28. D. Cassani, C. Tarsi and J. Zhang, Bounds for best constants in subcritical Sobolev embeddings, Nonlinear Anal. 187 (2019), 438–449. 29. D. Cassani, J. Van Schaftingen and J. Zhang, Groundstates for Choquard type equations with Hardy–Littlewood–Sobolev lower critical exponent, Proc. Roy. Soc. Edinburgh Sect. A. 150 (2018/2020), 1377–1400. 30. D. Cassani, H. Tavares and J. Zhang, Bose fluids and positive solutions of weakly coupled systems with critical growth in dimension two, J. Differential Equations 269 (2020), 2328–2385. 31. D. Cassani and D. Schiera, Uniqueness results for higher order Lane-Emden systems, Nonlinear Anal. 198 (2020), 17 pp. 32. D. Cassani and Y. Wang and J. Zhang, A unifed approach to singularly perturbed quasilinear Schrödinger equations, Milan J. Math. 88 (2020), 507–534. 33. D. Cassani, L. Vilasi and Y. Wang, Local vs nonlocal elliptic equations: short-long range field interactions, Adv. Nonlinear Anal. 10 (2021), 895–921. 34. D. Cassani, L. Vilasi and J. Zhang, Concentration phenomena at saddle points of potential for Schrödinger-Poisson systems, Comm. Pure Appl. Anal. 20 (2021), 1737-1754. 35. M. Tarsia, D. Cassani and A. Mira, On the Mathematical Foundation of Approximate Bayesian Computation–A Robust Set for Estimating Mechanistic Network Mod- els, https://www.uninsubria.it/sites/default/files/allegati/costnet. 20_paper_0.pdf 36. D. Cassani and Y. Wang, Asymptotic behavior of ground states and local uniqueness for fractional Schrödinger equations with nearly critical growth, Potential Anal. (2021), 40 pp. 37. D. Cassani and Y. Wang, Blow-up phenomena and asymptotic profiles passing from H1-critical to super-critical quasilinear Schrödinger equations, Adv. Nonlinear Stud. 21 (2021), 855–874. 38. D. Cassani and C. Tarsi, Schrödinger–Newton equations in dimension two via a Pohozaev–Trudinger log-weighted inequality, Calc. Var. Partial Differential Equa- tions 60:197 (2021). 39. D. Cassani and A. Tarsia, Maximum Principle for Higher Order Operators in General Domains, Adv. Nonlinear Anal. (2022). 40. C. Bucur, D. Cassani and C. Tarsi, Quasilinear logarithmic Choquard equations with exponential growth in RN , preprint 2021.

Survey contributions:

41. Series Le Garzantine, MATEMATICA, Garzanti (2014), pp. 1536. Editors: Maraschini-Palma, Scientific Revisor: D. Cassani. ISBN 978-88-11-50525-9

42. D. Cassani, L. Fattorusso and A. Tarsia, Nonlocal singular problems and applications to MEMS, IAENG, Proceedings of the World Congress on Engineering Vol. II (2013).

43. D. Cassani, Lemmi: Equazione di Eulero-Lagrange; Equazioni ellittiche non lin- eari; Metodo del moving plane; Metodo di concentrazione-compattezza; Principio variazionale; Problemi di omogeneizzazione; Punti stazionari, Enciclopedia della Scienza e della Tecnica, vol. VI, Ist. Enciclopedia Italiana fondata da G. Treccani (2008).