2022/11/03 by Irshaad Ahmed, Alberto Fıorenza, Ahmed, Irshaad +9
Mathematics · #35B45 #35D30 #35J25 #46B70 #46E30 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2211.01574
openalex publication_date 2022/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As in the work of Tartar ( Tartar L. Interpolation non linéaire et régularité, 9, Journal of Functional Analysis, (1972), 469-489) we developed here some new results on non linear interpolation of α-Hölderian mappings between normed spaces, namely, by studying the action of the mappings on K-functionals and between interpolation spaces with logarithm functors. We apply those results to obtain regularity results on the gradient of the solution to quasilinear equations of the form -div(\widehat a(∇ u ))+V(u)=f, whenever V is a nonlinear potential, f belongs to non standard spaces as Lorentz-Zygmund spaces. We show among other that the mapping T: Tf=∇ u is locally or globally α-Hölderian under suitable values of α and adequate hypothesis on V and \widehat a.