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Abstract
We present some regularity results on the gradient of the weak or entropic-renormalized solution u to the homogeneous Dirichlet problem for the quasilinear equations of the form
-div (|∇u|p-2 ∇u) + V(x;u) = f,
where Ω is a bounded smooth domain of ℝn, V is a nonlinear potential and f belongs to non-standard spaces like Lorentz-Zygmund spaces.
The results, which have been exposed by the third author in a talk presented in AGMA 2024, the International Scientific Online Conference «Algebraic and geometric methods of analysis», May 27-30, 2024, Ukraine, constitute only a part of results proved in detail in a paper coauthored with I. Ahmed, A. Fiorenza, A. Gogatishvili, A. El Hamidi and J.-M. Rakotoson [Analysis Mathematica, 49(4):895-950, 2023]
Moreover, we collect some well-known and new results of the identication of some interpolation spaces and we enrich some contents with details.
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