2025

Karppinen, Arttu; Sarsa, Saara

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 ∈ 𝑊 1,2 loc . This work contributes to the building up of quantitative second order Sobolev regularity for solutions of nonlinear equations.