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dc.contributor.authorDoležalová, Anna
dc.contributor.authorKangasniemi, Ilmari
dc.contributor.authorOnninen, Jani
dc.date.accessioned2023-11-23T10:00:08Z
dc.date.available2023-11-23T10:00:08Z
dc.date.issued2024
dc.identifier.citationDoležalová, A., Kangasniemi, I., & Onninen, J. (2024). Mappings of generalized finite distortion and continuity. <i>Journal of the London Mathematical Society</i>, <i>109</i>(1), Article e12835. <a href="https://doi.org/10.1112/jlms.12835" target="_blank">https://doi.org/10.1112/jlms.12835</a>
dc.identifier.otherCONVID_194528215
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/92048
dc.description.abstractWe study continuity properties of Sobolev mappings𝑓∈𝑊1,𝑛loc(Ω,ℝ𝑛),𝑛⩾2, that satisfy the following generalized finite distortion inequality||𝐷𝑓(𝑥)||𝑛⩽𝐾(𝑥)𝐽𝑓(𝑥) + Σ(𝑥)for almost every𝑥∈ℝ𝑛.Here𝐾∶ Ω→[1,∞)andΣ∶ Ω→[0,∞)are measurable functions. Note that whenΣ≡0, we recover the class of mappings of finite distortion, which are always continuous. The continuity of arbitrary solutions, however, turns out to be an intricate question. We fully solve the continuity problem in the case of bounded distortion𝐾∈𝐿∞(Ω), where a sharp condition for continuity is thatΣis in the Zygmund spaceΣlog𝜇(𝑒 + Σ) ∈ 𝐿1loc(Ω)for some𝜇>𝑛−1.We also show that one can slightly relax the boundedness assumption on𝐾to an exponential class exp(𝜆𝐾) ∈𝐿1loc(Ω)with𝜆>𝑛+1, and still obtain continuous solutions when Σlog𝜇(𝑒 + Σ) ∈ 𝐿1loc(Ω)with𝜇>𝜆. On the other hand, for all𝑝,𝑞 ∈ [1,∞] with 𝑝−1+𝑞−1=1, we construct a discontinuous solution with 𝐾∈𝐿𝑝loc(Ω)andΣ∕𝐾 ∈ 𝐿𝑞loc(Ω), including an example withΣ∈𝐿∞loc(Ω)and𝐾∈𝐿1loc(Ω).en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherWiley-Blackwell
dc.relation.ispartofseriesJournal of the London Mathematical Society
dc.rightsCC BY-NC-ND 4.0
dc.titleMappings of generalized finite distortion and continuity
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202311238064
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineAnalyysin ja dynamiikan tutkimuksen huippuyksikköfi
dc.contributor.oppiaineMathematicsen
dc.contributor.oppiaineAnalysis and Dynamics Research (Centre of Excellence)en
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.relation.issn0024-6107
dc.relation.numberinseries1
dc.relation.volume109
dc.type.versionpublishedVersion
dc.rights.copyright© 2023 the Authors
dc.rights.accesslevelopenAccessfi
dc.subject.ysoepäyhtälöt
dc.subject.ysofunktioteoria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p15720
jyx.subject.urihttp://www.yso.fi/onto/yso/p18494
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi10.1112/jlms.12835
jyx.fundinginformationGA CR, Grant/Award Number:P201/21-01976S; Schemes at CU,Grant/Award Number:CZ.02.2.69/0.0/0.0/19 073/0016935; NSF,Grant/Award Number: DMS-2154943
dc.type.okmA1


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