Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations

Cyril Imbert
Centre National de la Recherche Scientifique (CNRS)

In a joint work with G. Barles, E. Chasseigne and A. Ciomaga, we establish Holder and Lipschitz estimates for solutions of elliptic nonlinear integro-differential equations, by the classical Ishii-Lions's method. The main novelty lies in the type of nonlocal equations we can deal with: they can be degenerate both in the local and nonlocal term, e.g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one. Such equations are referred to as mixed integro-differential equations.

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