8.2020 - Lipschitz regularity for integro-differential PDE with coercive Hamiltonians

Lipschitz regularity for integro-differential PDE
with coercive Hamiltonians
Internship: IRMAR, Rennes
Olivier Ley
March 2021

        The goal is to study Lipschitz regularity estimates for solutions to non-
linear integro-differential PDEs. More precisely, the internship consists in

•  Learning the notion of viscosity solutions for integro-differential PDEs

        of fractional Laplacian type, see [1].

• reading and understanding the generalized Bernstein method devel-

       oped in [2]. This is the core of the internship and a further step would
       be to extend this approach to more general integro-differential PDEs.

References:
[1] Guy Barles and Cyril Imbert. Second-order elliptic integro-differential
equations: viscosity solutions' theory revisited. Ann. Inst. H. Poincaré
Anal. Non Linéaire, 25(3):567 - 585, 2008.
[2] Guy Barles, Olivier Ley, and Erwin Topp. Lipschitz regularity for integro-
differential equations with coercive Hamiltonians and applica- tion to large
time behavior. Nonlinearity, 30(2):703 - 734, 2017.