Research

RESEARCH TOPICS:


More in detail, during my PhD years, I carried out research on some problems  related to prescribing curvature in Conformal Geometry,  and I dealt with Mean-Field Games models with Choquard-type interaction. 

Now I’m investigating geometric aspects of PDEs in connection with the underlying curvature assumptions and geometric flows.



Publications:


1- Bernardini C. :  Existence and Compactness of Conformal Metrics on the Plane with Unbounded and Sign-Changing Gaussian Curvature, Vietnam J. Math. (2021). DOI:10.1007/s10013-021-00540-5 2 (preprint Arxiv: 2304.14305).

2- Bernardini C. :  Existence and asymptotic behavior of non-normal conformal metrics on R⁴ with sign-changing Q-curvature, Commun. Contemp. Math. 25 (2023), no. 10, Paper No. 2250053. DOI:10.1142/S0219199722500535 (preprint ArXiv: 2112.10848) .

3- Bernardini C., Vespri V., Zaccaron M. :   A note on Campanato’s L^p -regularity with continuous coefficients,  Eurasian Math. J.  13 (2022) no. 4 , 44 – 53.  DOI:10.32523/2077-9879-2022-13-4-44-53.

4- Bernardini C., Cesaroni A.:  Ergodic Mean-Field Games with aggregation of Choquard-type, J. Differential Equations 364 (2023) 296-335. DOI:10.1016/j.jde.2023.03.045 (preprint ArXiv: 2208.08177).

5- Bernardini C.:  Mass concentration for Ergodic Choquard Mean-Field Games, (2022) accepted for publication in ESAIM: COCV (preprint ArXiv:2212.00132).


Preprint:

6-Bernardini C., Cesaroni A. :  Boundary value problems for Choquard equations, (2023) submitted (preprint Arxiv: 2305.09043)