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dc.contributor.authorSiljander, Juhana
dc.contributor.authorWang, Changyou
dc.contributor.authorZhou, Yuan
dc.date.accessioned2017-01-12T12:20:48Z
dc.date.available2017-11-02T22:45:11Z
dc.date.issued2017
dc.identifier.citationSiljander, J., Wang, C., & Zhou, Y. (2017). Everywhere differentiability of viscosity solutions to a class of Aronsson's equations. <i>Annales de l'Institut Henri Poincare (C). Analyse non Lineaire</i>, <i>34</i>(1), 119-138. <a href="https://doi.org/10.1016/j.anihpc.2015.10.003" target="_blank">https://doi.org/10.1016/j.anihpc.2015.10.003</a>
dc.identifier.otherCONVID_25279683
dc.identifier.otherTUTKAID_67705
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/52712
dc.description.abstractWe show the everywhere differentiability of viscosity solutions to a class of Aronsson equations in R n for n ≥ 2, where the coefficient matrices A are assumed to be uniformly elliptic and C 1,1 . Our result extends an earlier important theorem by Evans and Smart [19] who have studied the case A = In which correspond to the ∞-Laplace equation. We also show that every point is a Lebesgue point for the gradient. In the process of proving the results we improve some of the gradient estimates obtained for the infinity harmonic functions. The lack of suitable gradient estimates has been a major obstacle for solving the C 1,α problem in this setting, and we aim to take a step towards better understanding of this problem, too. A key tool in our approach is to study the problem in a suitable intrinsic geometry induced by the coefficient matrix A. Heuristically, this corresponds to considering the question on a Riemannian manifold whose the metric is given by the matrix A.
dc.language.isoeng
dc.publisherElsevier Masson
dc.relation.ispartofseriesAnnales de l'Institut Henri Poincare (C). Analyse non Lineaire
dc.subject.otherL∞-variational problem
dc.subject.otherabsolute minimizer
dc.subject.othereverywhere differentiability
dc.subject.otherAronsson's equation
dc.titleEverywhere differentiability of viscosity solutions to a class of Aronsson's equations
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201701101123
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.updated2017-01-10T16:15:04Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange119-138
dc.relation.issn0294-1449
dc.relation.numberinseries1
dc.relation.volume34
dc.type.versionacceptedVersion
dc.rights.copyright© 2015 Elsevier Masson SAS. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.1016/j.anihpc.2015.10.003


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