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Hardy inequalities, Rellich inequalities and local Dirichlet forms

dc.contributor.authorRobinson, Derek
dc.date.accessioned2019-06-06T00:45:07Z
dc.date.issued2018
dc.date.updated2019-03-24T07:16:36Z
dc.description.abstractFirst, the Hardy and Rellich inequalities are defined for the sub-Markovian operator associated with a local Dirichlet form. Secondly, two general conditions are derived which are sufficient to deduce the Rellich inequality from the Hardy inequality. In addition, the Rellich constant is calculated from the Hardy constant. Thirdly, we establish that the criteria for the Rellich inequality are verified for a large class of weighted second-order operators on a domain Ω⊆Rd . The weighting near the boundary ∂Ω can be different from the weighting at infinity. Finally, these results are applied to weighted second-order operators on Rd∖{0} and to a general class of operators of Grushin type.en_AU
dc.format.mimetypeapplication/pdfen_AU
dc.identifier.issn1424-3199en_AU
dc.identifier.urihttp://hdl.handle.net/1885/163974
dc.language.isoen_AUen_AU
dc.publisherSpringer Verlagen_AU
dc.rights© 2018 Springer International Publishing AG, part of Springer Natureen_AU
dc.sourceJournal of Evolution Equationsen_AU
dc.titleHardy inequalities, Rellich inequalities and local Dirichlet formsen_AU
dc.typeJournal articleen_AU
local.bibliographicCitation.lastpage1541en_AU
local.bibliographicCitation.startpage1521en_AU
local.contributor.affiliationRobinson, Derek, College of Science, ANUen_AU
local.contributor.authoruidRobinson, Derek, u8200089en_AU
local.description.embargo2037-12-31
local.description.notesImported from ARIESen_AU
local.identifier.absfor010110 - Partial Differential Equationsen_AU
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciencesen_AU
local.identifier.ariespublicationa383154xPUB10102en_AU
local.identifier.citationvolume18en_AU
local.identifier.doi10.1007/s00028-018-0454-2en_AU
local.identifier.scopusID2-s2.0-85047665063
local.publisher.urlhttps://link.springer.comen_AU
local.type.statusPublished Versionen_AU

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