The Dirichlet problem for the total variation flow

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dc.contributor.authorAndreu, Fuensanta
dc.contributor.authorBallester, Coloma
dc.contributor.authorCaselles, Vicente
dc.contributor.authorMazón, José
dc.date.accessioned2018-12-19T13:51:40Z
dc.date.available2018-12-19T13:51:40Z
dc.date.issued2001
dc.description.abstractWe introduce a new concept of solution for the Dirichlet problem for the total variational flow named entropy solution. Using Kruzhkov's method of doubling variables both in space and in time we prove uniqueness and a comparison principle in L1 for entropy solutions. To prove the existence we use the nonlinear semigroup theory and we show that when the initial and boundary data are nonnegative the semigroup solutions are strong solutions.
dc.description.sponsorshipThe first and fourth authors have been partially supported by the Spanish DGICYT, Project PB98-1442. The second and third authors acknowledge partial support by the TMR European Project "Viscosity Solutions and their Applications'' reference FMRX-CT98-0234.
dc.format.mimetypeapplication/pdf
dc.identifier.citationAndreu F, Ballester C, Caselles V, Mazón JM. The Dirichlet problem for the total variation flow. J Funct Anal. 2001 Mar 10;180(2):347-403. DOI: 10.1006/jfan.2000.3698
dc.identifier.doihttp://dx.doi.org/10.1006/jfan.2000.3698
dc.identifier.issn0022-1236
dc.identifier.urihttp://hdl.handle.net/10230/36150
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofJournal of Functional Analysis. 2001 Mar 10;180(2):347-403.
dc.rights© Elsevier http://dx.doi.org/10.1006/jfan.2000.3698
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.titleThe Dirichlet problem for the total variation flow
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/acceptedVersion

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