Adjoint methods for nonlinear PDEs: from Hamilton-Jacobi equations to Mean Field Games

18 marzo 2019
18 marzo 2019
Contatti: 
Staff Dipartimento Economia e Management
Via Inama, 5
Tel. 
0461 282239 - 2126 - 3936 - 2238
Fax 
0461 282241

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
Ore: 15:00

Relatore:

  • Alessandro Goffi  (Gran Sasso Science Institute)

Abstract:

In this talk, I will discuss recent developments on regularity properties for solutions to Hamilton-Jacobi PDEs via duality methods obtained in collaboration with M. Cirant. In par- ticular, the seminar will be mainly devoted to consider Lipschitz regularity of solutions to time- dependent viscous Hamilton-Jacobi equations with superlinear growth in the gradient and data in Lebsgue spaces. This analysis is partially motivated by problems arising in Mean-Field Game theory, where solutions of the so-called Mean Field Game equations are related to an optimal con- trol problem for Hamilton-Jacobi-type PDEs having a right-hand side bounded in some Lebesgue norm. The result is accomplished by exploiting regularity properties of the gradient of solutions to a (dual) Fokker-Planck equation.
Finally, I will present further applications of this scheme to prove qualitative properties of solu- tions to parabolic problems with fractional diffusion.

Referente: Andrea Pinamonti