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arXiv · 1803.01835

Nonlocal operators with singular anisotropic kernels

Jamil Chaker·Moritz Kassmann
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Abstract

We study nonlocal operators acting on functions in the Euclidean space. The operators under consideration generate anisotropic jump processes, e.g., a jump process that behaves like a stable process in each direction but with a different index of stability. Its generator is the sum of one-dimensional fractional Laplace operators with different orders of differentiability. We study such operators in the general framework of bounded measurable coefficients. We prove a weak Harnack inequality and H\"older regularity results for solutions to corresponding integro-differential equations.

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Jamil Chaker, Moritz Kassmann. 2018-03-05. Nonlocal operators with singular anisotropic kernels. https://arxiv.org/abs/1803.01835

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