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dc.contributor.authorIwaniec, Tadeusz
dc.contributor.authorOnninen, Jani
dc.date.accessioned2020-01-31T10:53:00Z
dc.date.available2020-01-31T10:53:00Z
dc.date.issued2019
dc.identifier.citationIwaniec, T., & Onninen, J. (2019). Radó-Kneser-Choquet Theorem for simply connected domains (p-harmonic setting). <i>Transactions of the American Mathematical Society</i>, <i>371</i>(4), 2307-2341. <a href="https://doi.org/10.1090/tran/7348" target="_blank">https://doi.org/10.1090/tran/7348</a>
dc.identifier.otherCONVID_28893104
dc.identifier.otherTUTKAID_80493
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/67665
dc.description.abstractA remarkable result known as Rad´o-Kneser-Choquet theorem asserts that the harmonic extension of a homeomorphism of the boundary of a Jordan domain ⌦ ⇢ R2 onto the boundary of a convex domain Q ⇢ R2 takes ⌦ di↵eomorphically onto Q . Numerous extensions of this result for linear and nonlinear elliptic PDEs are known, but only when ⌦ is a Jordan domain or, if not, under additional assumptions on the boundary map. On the other hand, the newly developed theory of Sobolev mappings between Euclidean domains and Riemannian manifolds demands to extend this theorem to the setting on simply connected domains. This is the primary goal of our article. The class of the p -harmonic equations is wide enough to satisfy those demands. Thus we confine ourselves to considering the p -harmonic mappings. The situation is quite di↵erent than that of Jordan domains. One must circumvent the inherent topological diculties arising near the boundary. Our main Theorem 4 is the key to establishing approximation of monotone Sobolev mappings with di↵eomorphisms. This, in turn, leads to the existence of energy-minimal deformations in the theory of Nonlinear Elasticity. Hence the usefulness of Theorem 4. We do not enter these applications here, but refer the reader to Section 1.2, for comments. .fi
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAmerican Mathematical Society
dc.relation.ispartofseriesTransactions of the American Mathematical Society
dc.rightsCC BY-NC-ND 4.0
dc.subject.otherharmonic mappings
dc.subject.otherp-harmonic equation
dc.subject.othermonotone mappings
dc.titleRadó-Kneser-Choquet Theorem for simply connected domains (p-harmonic setting)
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202001301868
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2020-01-30T07:15:18Z
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange2307-2341
dc.relation.issn0002-9947
dc.relation.numberinseries4
dc.relation.volume371
dc.type.versionacceptedVersion
dc.rights.copyright© 2018 American Mathematical Society
dc.rights.accesslevelopenAccessfi
dc.subject.ysofunktioteoria
dc.subject.ysofunktionaalianalyysi
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p18494
jyx.subject.urihttp://www.yso.fi/onto/yso/p17780
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi10.1090/tran/7348
dc.type.okmA1


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