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 editorsKarppinen, Arttu; Sarsa, Saara

Journal or seriesNonlinear Analysis: Theory, Methods and Applications

ISSN0362-546X

eISSN1873-5215

Publication year2025

Volume253

Article number113737

PublisherElsevier

Publication countryUnited Kingdom

Publication languageEnglish

DOIhttps://doi.org/10.1016/j.na.2024.113737

Publication open accessOpenly available

Publication channel open accessPartially 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.


Keywordspartial differential equations

Free keywordsOrlicz–Laplace equation; Sobolev regularity


Contributing organizations


Ministry reportingYes

VIRTA submission year2025

Preliminary JUFO rating1


Last updated on 2025-25-01 at 20:05