dc.contributor.author | Lehrbäck, Juha | |
dc.contributor.author | Robinson, Derek W. | |
dc.date.accessioned | 2015-12-14T12:06:32Z | |
dc.date.available | 2015-12-14T12:06:32Z | |
dc.date.issued | 2016 | |
dc.identifier.citation | Lehrbäck, J., & Robinson, D. W. (2016). Uniqueness of diffusion on domains with rough boundaries. <i>Nonlinear Analysis: Theory, Methods and Applications</i>, <i>131</i>, 60-80. <a href="https://doi.org/10.1016/j.na.2015.09.007" target="_blank">https://doi.org/10.1016/j.na.2015.09.007</a> | |
dc.identifier.other | CONVID_25351335 | |
dc.identifier.other | TUTKAID_68097 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/48090 | |
dc.description.abstract | Let 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.iso | eng | |
dc.publisher | Elsevier Ltd. | |
dc.relation.ispartofseries | Nonlinear Analysis: Theory, Methods and Applications | |
dc.subject.other | Ahlfors regularity | |
dc.subject.other | Hardy inequality | |
dc.subject.other | Markov uniqueness | |
dc.title | Uniqueness of diffusion on domains with rough boundaries | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-201512144008 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.contributor.oppiaine | Matematiikka | fi |
dc.contributor.oppiaine | Mathematics | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.date.updated | 2015-12-14T10:15:16Z | |
dc.type.coar | journal article | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 60-80 | |
dc.relation.issn | 0362-546X | |
dc.relation.numberinseries | 0 | |
dc.relation.volume | 131 | |
dc.type.version | submittedVersion | |
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.accesslevel | openAccess | fi |
dc.relation.doi | 10.1016/j.na.2015.09.007 | |