The Total variation flow in RN

Mostra el registre complet Registre parcial de l'ítem

• dc.contributor.author Bellettini, Giovanni
• dc.contributor.author Caselles, Vicente
• dc.contributor.author Novaga, Matteo
• dc.date.accessioned 2018-12-20T15:29:41Z
• dc.date.available 2018-12-20T15:29:41Z
• dc.date.issued 2002
• dc.description.abstract In this paper, we study the minimizing total variation flow ut=div(Du/∣Du∣) in N for initial data u0 in Lloc1(N), proving an existence and uniqueness result. Then we characterize all bounded sets Ω of finite perimeter in 2 which evolve without distortion of the boundary. In that case, u0=χΩ evolves as u(t,x)=(1−λΩt)+χΩ, where χΩ is the characteristic function of Ω, λΩ≔P(Ω)/∣Ω∣, and P(Ω) denotes the perimeter of Ω. We give examples of such sets. The solutions are such that v≔λΩχΩ solves the eigenvalue problem −div. We construct other explicit solutions of this problem. As an application, we construct explicit solutions of the denoising problem in image processing.en
• dc.description.sponsorship We acknowledge partial support by the TMR European Project ‘Viscosity Solutions and their Applications,’ reference FMRX-CT98-0234. The second author acknowledges partial support by the PNPGC project, reference BFM2000-0962-C02-01.
• dc.format.mimetype application/pdf
• dc.identifier.citation Bellettini G, Caselles V, Novaga M. The total variation flow in RN. J Differ Equ. 2002 Sep 20;184(2):475-525. DOI: 10.1006/jdeq.2001.4150
• dc.identifier.doi http://dx.doi.org/10.1006/jdeq.2001.4150
• dc.identifier.issn 0022-0396
• dc.identifier.uri http://hdl.handle.net/10230/36163
• dc.language.iso eng
• dc.publisher Elsevier
• dc.relation.ispartof Journal of Differential Equations. 2002 Sep 20;184(2):475-525.
• dc.rights © Elsevier http://dx.doi.org/10.1006/jdeq.2001.4150
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Total variation flow
• dc.subject.keyword Nonlinear parabolic equations
• dc.subject.keyword Finite perimeter sets
• dc.subject.keyword Calibrable sets
• dc.title The Total variation flow in RN
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion