In this short course, I will address some regularity aspects in the theory of Mean-Field Games systems, with special emphasis on stationary and uniformly elliptic problems. I will first describe some regularity results for linear uniformly elliptic PDEs and semi-linear PDEs of Hamilton-Jacobi type. Then, I will show how to use these tools to prove the existence (and in some cases uniqueness) of solutions to MFG systems.
Marco Cirant is an Assistant Professor at the University of Padova. He received his Ph.D. in Mathematics from the University of Padova in 2014 and did his Post-Doc at the University of Milano. Then, he has been an Assistant Professor at the University of Parma in 2019. Cirant's research interests are in partial differential equations, in particular in semi-linear and fully-nonlinear elliptic PDEs and systems arising in Mean-Field Games models.