Hölder and Harnack estimates for integro-differential operators with kernels of measure

Abstract

We establish Hölder and Harnack estimates for weak solutions of a class of elliptic nonlocal equations that are modeled on integro-differential operators with kernels of measure. The approach is of De Giorgi-type, as developed by DiBenedetto, Gianazza and Vespri in a local setting. Our results generalize the work by Dyda and Kassmann (2020).