A1 Journal article (refereed)
On the heterogeneous distortion inequality (2022)
Kangasniemi, I., & Onninen, J. (2022). On the heterogeneous distortion inequality. Mathematische Annalen, 384(3-4), 1275-1308. https://doi.org/10.1007/s00208-021-02315-2
JYU authors or editors
Publication details
All authors or editors: Kangasniemi, Ilmari; Onninen, Jani
Journal or series: Mathematische Annalen
ISSN: 0025-5831
eISSN: 1432-1807
Publication year: 2022
Publication date: 29/11/2021
Volume: 384
Issue number: 3-4
Pages range: 1275-1308
Publisher: Springer
Publication country: Germany
Publication language: English
DOI: https://doi.org/10.1007/s00208-021-02315-2
Publication open access: Not open
Publication channel open access:
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2102.03471
Additional information: Correction to: On the heterogeneous distortion inequality
http://dx.doi.org/10.1007/s00208-023-02728-1
Abstract
We study Sobolev mappings f∈Wloc1,n(Rn,Rn), n≥2, that satisfy the heterogeneous distortion inequality |Df(x)|n≤KJf(x)+σn(x)|f(x)|n for almost every x∈Rn. Here K∈[1,∞) is a constant and σ≥0 is a function in Llocn(Rn). Although we recover the class of K-quasiregular mappings when σ≡0, the theory of arbitrary solutions is significantly more complicated, partly due to the unavailability of a robust degree theory for non-quasiregular solutions. Nonetheless, we obtain a Liouville-type theorem and the sharp Hölder continuity estimate for all solutions, provided that σ∈Ln−ε(Rn)∩Ln+ε(Rn) for some ε>0. This gives an affirmative answer to a question of Astala, Iwaniec and Martin.
Keywords: complex analysis; partial differential equations; differential geometry; inequalities (mathematics)
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2022
JUFO rating: 2