5 papers · 2 filters
A strongly degenerate fully nonlinear mean field game with nonlocal diffusion
Indranil Chowdhury, Espen R. Jakobsen, MiÅosz Krupski
There are few results on mean field game (MFG) systems where the PDEs are either fully nonlinear or have degenerate diffusions. This paper introduces a problem that combines both d…
On fully nonlinear parabolic mean field games with nonlocal and local diffusions
Indranil Chowdhury, Espen R. Jakobsen, MiÅosz Krupski
We introduce a class of fully nonlinear mean field games posed in . We justify that they are related to controlled local or nonlocal diffusions, and more g…
A Deep BSDE approximation of nonlinear integro-PDEs with unbounded nonlocal operators
Espen Robstad Jakobsen, Sehail Mazid
Machine learning for partial differential equations (PDEs) is a hot topic. In this paper we introduce and analyse a Deep BSDE scheme for nonlinear integro-PDEs with unbounded nonlo…
Optimal stability results and nonlinear duality for entropy and viscosity solutions
Nathaël Alibaud, Jørgen Endal, Espen Robstad Jakobsen
We give a new and rigorous duality relation between two central notions of weak solutions of nonlinear PDEs: entropy and viscosity solutions. It takes the form of the nonlinear dua…
Towards a Schauder theory for fractional viscous Hamilton--Jacobi equations
Espen R. Jakobsen, Artur Rutkowski
We survey some results on Lipschitz and Schauder regularity estimates for viscous Hamilton--Jacobi equations with subcritical Lévy diffusions. The Schauder estimates, along with e…