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We prove a higher regularity result for weak solutions to nonlinear nonlocalequations along the integrability scale of Bessel potential spaces $H^{s,p}$under a mild continuity assumption on the kernel. By embedding, this alsoyields regularity in Sobolev-Slobodeckij spaces $W^{s,p}$. Our approach isbased on a characterization of Bessel potential spaces in terms of a certainnonlocal gradient-type operator and a perturbation approach commonly used inthe context of local elliptic equations in divergence form.

Higher integrability for nonlinear nonlocal equations with irregular kernel