Weak solutions of the nonlocal (1,p)-Laplace equation in the superquadratic case p≥2 are shown to lie in W^{γ,q}_{loc} for γ< spp/(p−1), and to have a gradient in L^q_{loc} when sp>(p−1)/p.
Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann
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Sobolev regularity for the nonlocal $(1, p)$-Laplace equations in the superquadratic case
Weak solutions of the nonlocal (1,p)-Laplace equation in the superquadratic case p≥2 are shown to lie in W^{γ,q}_{loc} for γ< spp/(p−1), and to have a gradient in L^q_{loc} when sp>(p−1)/p.