A quantitative second order Sobolev regularity for (inhmogeneous) normalized p(⋅)-Laplace equations

2024/03/06 by Yuqing Wang, Yuan Zhou, Wang, Yuqing +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2403.03784

openalex publication_date 2024/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω be a domain of \mathbb Rⁿ with n≥ 2 and p(⋅) be a local Lipschitz funcion in Ω with 11 and sup_Up(x)<3+\frac2n-2, one has D²u∈ L^2+δ(U) locally with a quantitative upper bound, and also with a pointwise upper bound |D²u|²≤ -C∑_1≤ i0 and C≥ 1 are independent of u. These extend the related results obtaind by Adamowicz-Hästö \citeAH2010 when n=2 and β=0.

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