Estimates for $p$-Laplace type equation in a limit case

We study some Dirichlet problem for a $p$--Laplacian type operator in the setting of Orlicz--Zygmund space $L^q\log^{-α}L(Ω,\mathbb R^N)$, $q >1$ and $α>0$. More precisely, our aim is to establish which assuptions on the parameter $α>0$ lead to existence, uniqueness of the solution and continuity of the associated nonlinear operator.

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