Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations

Understand

We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method.

• We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011).
• In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations.
• These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g.