2023/08/08 by Arttu Karppinen, Karppinen, Arttu, Saara Sarsa +1
Computer Science · Mathematics · #35J62 #35J70 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2308.04038
openalex publication_date 2023/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Orlicz--Laplace equation -div((φ'(|∇ u|))/(|∇ u|)∇ u)=f where φ is an Orlicz function and either f=0 or f∈ L^∞. We prove local second order regularity results for the weak solutions u of the Orlicz--Laplace equation. More precisely, we show that if ψ is another Orlicz function that is close to φ in a suitable sense, then (ψ'(|∇ u|))/(|∇ u|)∇ u∈ W1,2loc. This work contributes to the building up of quantitative second order Sobolev regularity for solutions of nonlinear equations.