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

Abstract

We study the Dirichlet problem for a $p$-Laplacian type operator in the setting of the Orlicz–Zygmund space ${\mathcal{L}}^q{\log }^{-\alpha }\mathcal{L}\left(\Omega ,{\mathbb{R}}^N\right)$, $q>1$ and $\alpha >0$. More precisely, our aim is to establish under which assuptions on $\alpha >0$ existence and uniqueness of the solution are assured.