Existence and uniqueness of a renormalized solution to fractional elliptic inclusions with L¹-data

Let d ∈ and Ω ⊂ ᵈ be bounded with Lipschitz boundary. We prove the existence and uniqueness of a renormalized solution to the inclusion problem \[ {cases} β(u) + Lu f & in Ω, \\ u = 0 & in Ω, {cases} \] where f ∈ L¹(Ω), the operator L generalizes the regional fractional p-Laplacian with 1 < p < ∞ and β is a maximal monotone operator on . A comparison between renormalized and weak solutions is also discussed.