Regularity for fully nonlinear integro-differential operators with kernels of variable orders. (April 2020) - Kim, Minhyun; Lee, Ki-Ahm
Abstract: We consider fully nonlinear elliptic integro-differential operators with kernels of variable orders, which generalize the integro-differential operators of the fractional Laplacian type in Caffarelli and Silvestre (2009). Since the order of differentiability of the kernel is not characterized by a single number, we use the constant C φ = ∫ R n 1 − cos y 1 | y | n φ ( | y | ) d y − 1 instead of 2 − σ, where φ satisfies a weak scaling condition. We obtain the uniform Harnack inequality and Hölder estimates of viscosity solutions to the nonlinear integro-differential equations.