Intrinsic scaling properties for nonlocal operators II

Abstract

We study integrodifferential operators and regularity estimates for solutions to integrodifferential equations. Our emphasis is on kernels with a critically low singularity which does not allow for standard scaling. For example, we treat operators that have a logarithmic order of differentiability. For corresponding equations we prove a growth lemma and derive a priori estimates. We derive these estimates by classical methods developed for partial differential operators. Since the integrodifferential operators under consideration generate Markov jump processes, we are able to offer an alternative approach using probabilistic techniques.

The assumptions have slightly been weakened. The material of arXiv:1310.5371 has been integrated

References in corpus (4)

• Regularity for parabolic integro-differential equations with very irregular kernels
• Symmetry via antisymmetric maximum principles in nonlocal problems of variable order
• Hölder estimates for nonlocal-diffusion equations with drifts
• Regularity for fully nonlinear equations driven by spatial-inhomogeneous nonlocal operators

Cited by in corpus (6)

• Regularity for parabolic integro-differential equations with very irregular kernels
• On the domain of fractional Laplacians and related generators of Feller processes
• Nonlocal heat equations: decay estimates and Nash inequalities
• Hölder estimates for nonlocal-diffusion equations with drifts
• Hölder continuity of harmonic functions for Hunt processes with Green function
• Regularity for fully nonlinear integro-differential operators with regularly varying kernels