On the Hölder regularity for solutions of integro-differential equations like the anisotropic fractional Laplacian

Abstract

In this paper we study integro-differential equations like the anisotropic fractional Laplacian. As in [Silvestre, Indiana University Mathematics Journal 55, 2006], we adapt the De Giorgi technique to achieve the $C^{\gamma }$-regularity for solutions of class $C^2$ and use the geometry found in [Caffarelli, Leitão, and Urbano, Math. Ann. 360, 2014] to get an ABP estimate, a Harnack inequality and the interior $C^{1,\gamma }$ regularity for viscosity solutions.

arXiv admin note: text overlap with arXiv:1311.0795