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dc.contributor.authorLehrbäck, Juha
dc.contributor.authorRobinson, Derek W.
dc.date.accessioned2015-12-14T12:06:32Z
dc.date.available2015-12-14T12:06:32Z
dc.date.issued2016
dc.identifier.citationLehrbäck, J., & Robinson, D. (2016). Uniqueness of diffusion on domains with rough boundaries. <em>Nonlinear Analysis: Theory, Methods & Applications</em>, 131, 60-80. <a href="http://dx.doi.org/10.1016/j.na.2015.09.007">doi:10.1016/j.na.2015.09.007</a> Retrieved from <a href="http://arxiv.org/abs/1504.00127">http://arxiv.org/abs/1504.00127</a>
dc.identifier.otherTUTKAID_68097
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/48090
dc.description.abstractLet Ω be a domain in View the MathML source and View the MathML source a quadratic form on L2(Ω) with domain View the MathML source where the ckl are real symmetric L∞(Ω)-functions with C(x)=(ckl(x))>0 for almost all x∈Ω. Further assume there are a,δ>0 such that View the MathML source for dΓ≤1 where dΓ is the Euclidean distance to the boundary Γ of Ω. We assume that Γ is Ahlfors s-regular and if s, the Hausdorff dimension of Γ, is larger or equal to d−1 we also assume a mild uniformity property for Ω in the neighbourhood of one z∈Γ. Then we establish that h is Markov unique, i.e. it has a unique Dirichlet form extension, if and only if δ≥1+(s−(d−1)). The result applies to forms on Lipschitz domains or on a wide class of domains with Γ a self-similar fractal. In particular it applies to the interior or exterior of the von Koch snowflake curve in View the MathML source or the complement of a uniformly disconnected set in View the MathML source.
dc.language.isoeng
dc.publisherElsevier Ltd.
dc.relation.ispartofseriesNonlinear Analysis: Theory, Methods & Applications
dc.subject.otherAhlfors regularity
dc.subject.otherHardy inequality
dc.subject.otherMarkov uniqueness
dc.titleUniqueness of diffusion on domains with rough boundaries
dc.typearticle
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201512144008
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikka
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2015-12-14T10:15:16Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange60-80
dc.relation.issn0362-546X
dc.relation.volume131
dc.type.versionsubmittedVersion
dc.rights.copyright© 2015 Elsevier Ltd. This is an preprint version of an article whose final and definitive form has been published by Elsevier.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.1016/j.na.2015.09.007


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