Diff. Geom, Math. Phys., PDE Seminar: Gonzalo Dávila

We study the regularity of solutions of parabolic equations of the form u_t - Iu = f, where I is a fully non linear non local operator. We prove C^\alpha regularity in space and time and, under different assumptions on the kernels, C^{1,\alpha}; in space for translation invariant equations. The proofs rely on a weak parabolic ABP and the classic ideas of K. Tso and L. Wang. Our results remain uniform as  \sigma goes to 2 allowing us to recover most of the regularity results of the local case.
This is a joint work with Hector Chang Lara.