A1 Journal article (refereed)
On Limits at Infinity of Weighted Sobolev Functions (2022)

Eriksson-Bique, S., Koskela, P., & Nguyen, K. (2022). On Limits at Infinity of Weighted Sobolev Functions. Journal of Functional Analysis, 283(10), Article 109672. https://doi.org/10.1016/j.jfa.2022.109672

JYU authors or editors

Publication details

All authors or editorsEriksson-Bique, Sylvester; Koskela, Pekka; Nguyen, Khanh

Journal or seriesJournal of Functional Analysis



Publication year2022


Issue number10

Article number109672


Publication countryBelgium

Publication languageEnglish


Publication open accessOpenly available

Publication channel open accessPartially open access channel

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/82817

Web address of parallel published publication (pre-print)https://arxiv.org/abs/2201.10876v1

Additional informationDedicated to Professor Olli Martio on the occasion of his 80th birthday celebration.


We study necessary and sufficient conditions for a Muckenhoupt weight w∈Lloc1(Rd) that yield almost sure existence of radial, and vertical, limits at infinity for Sobolev functions u∈Wloc1,p(Rd,w) with a p-integrable gradient |∇u|∈Lp(Rd,w) where 1≤p<∞ and 2≤d<∞. The question is shown to subtly depend on the sense in which the limit is taken.
First, we fully characterize the existence of radial limits. Second, we give essentially sharp sufficient conditions for the existence of vertical limits. In the specific setting of product and radial weights, we give if and only if statements. These generalize and give new proofs for results of Fefferman and Uspenskiĭ.
As applications to partial differential equations, we give results on the limiting behavior of weighted q-Harmonic functions at infinity (1<∞), which depend on the integrability degree of its gradient.

Keywordsmathematicsdifferential equationsfunctions (mathematical methods)

Free keywordsSobolev functions; Muckenhoupt; limit; asymptotic

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Ministry reportingYes

Reporting Year2022

JUFO rating2

Last updated on 2024-03-04 at 19:17