Applications of Interpolation theory to the regularity of some equasilinear PDEs

2024/11/01 by Irshaad Ahmed, Alberto Fıorenza, Ahmed, Irshaad +7
Mathematics · #35B45 #35D30 #35J25 #35J62 #46B70 #46E30 #46M35 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2411.00367

openalex publication_date 2024/11/01 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28

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 -\rm div~(|∇ u|^p-2∇ u)+V(x;u)=f, where Ω is a bounded smooth domain of \mathbb Rⁿ, V is a nonlinear potential and f belongs to non-standard spaces like Lorentz-Zygmund spaces. Moreover, we collect some well-known and new results for identifying some interpolation spaces and enrich some contents with details.

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