A1 Journal article (refereed)
Local second order regularity of solutions to elliptic Orlicz–Laplace equation (2025)
Karppinen, A., & Sarsa, S. (2025). Local second order regularity of solutions to elliptic Orlicz–Laplace equation. Nonlinear Analysis: Theory, Methods and Applications, 253, Article 113737. https://doi.org/10.1016/j.na.2024.113737
JYU authors or editors
Publication details
All authors or editors: Karppinen, Arttu; Sarsa, Saara
Journal or series: Nonlinear Analysis: Theory, Methods and Applications
ISSN: 0362-546X
eISSN: 1873-5215
Publication year: 2025
Volume: 253
Article number: 113737
Publisher: Elsevier
Publication country: United Kingdom
Publication language: English
DOI: https://doi.org/10.1016/j.na.2024.113737
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/99423
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2308.04038
Abstract
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.
Keywords: partial differential equations
Free keywords: Orlicz–Laplace equation; Sobolev regularity
Contributing organizations
Ministry reporting: Yes
VIRTA submission year: 2025
Preliminary JUFO rating: 1