Applications of Interpolation theory to the regularity of some quasilinear PDEs

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 ([2]). Moreover, we collect some well-known and new results of the identication of some interpolation spaces and we enrich some contents with details.