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A regularity theory for parabolic equations with anisotropic non-local operators in spaces
In this paper, we present an -regularity theory for parabolic
equations of the form: Here,
represents anisotropic non-local operators
encompassing the singular anisotropic fractional Laplacian with measurable
coefficients: To address the anisotropy of the operator, we employ a probabilistic
representation of the solution and Calder\'on-Zygmund theory. As applications
of our results, we demonstrate the solvability of elliptic equations with
anisotropic non-local operators and parabolic equations with isotropic
non-local operators
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