Nonlinear interpolation of $\alpha$-Hölderian mappings with applications to quasilinear PDEs
A talk in the Nonlocal Equations: Analysis and Numerics series by
Amiran Gogatishvili from Prague
| Abstract: | We present some well-known and new results for identifying some interpolation spaces on nonlinear interpolation of α- H¨olderian mappings between
normed spaces. We apply these results to obtain 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 $- \mathrm{div} (a (\nabla u)) + V(u) = f$, where, $\Omega$ is a bounded smooth domain of $R^n$, $V$ is a nonlinear potential and $f$ belongs to non-standard spaces like Lorentz-Zygmund spaces. The presentation is based on the following papers: 1. I. Ahmed, A. Fiorenza, M.R. Formica, A. Gogatishvili, A. El Hamidi, J. M. Rakotoson, Quasilinear PDEs, interpolation spaces and Hölderian mappings, Anal. Math. 49 (2023), no. 4, 895–950. 2. I. Ahmed, A. Fiorenza, M.R. Formica, A. Gogatishvili, A. El Hamidi, J. M. Rakotoson, Applications of Interpolation theory to the regularity of some quasilinear PDEs.. Proceedings of the International Scientific Online Conference ”Algebraic and geometric methods of analysis, AGMA 2024 May 27-30, 2024, Ukraine, Proceedings of the International Geometry Center, 2024, 35 pages. Within the CRC this talk is associated to the project(s): A7 |