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Partitions with prescribed mean curvatures

Name: Partitions with prescribed mean curvatures
Creator: LEONARDI, Gian Paolo
Keywords: regularity, Caccioppoli partitions, 0103 physical sciences, Variational problems in a geometric measure-theoretic setting, Regularity of solutions in optimal control, variational image segmentation, Caccioppoli partitions; generalised mean curvature, prescribed mean curvature, Existence theories for free problems in two or more independent variables, 0101 mathematics

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2002 Italy Publisher:Springer Science and Business Media LLCJournal:manuscripta mathematica, volume 107, pages 111-133 (issn: 0025-2611, eissn: 1432-1785,

Authors: LEONARDI, Gian Paolo;

doi: 10.1007/s002290100230

handle: 11572/228730 , 11380/454165

Partitions with prescribed mean curvatures

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Abstract

The author considers a variational problem on Caccioppoli partitions with countably many components, which models immiscible fluids as well as variational image segmentation. The functional introduced by the author generalizes a previous one discussed by \textit{U. Massari} [Arch. Ration. Mech. Anal. 55, 357-382 (1974; Zbl 0305.49047); Rend. Sem. Mat. Univ. Padova 53(1975), 37-52 (1976; Zbl 0358.49019)] in connection with the study of sets with prescribed mean curvature. The paper provides existence as well as regularity results, moreover, some interesting examples are presented.

Country

Italy

Related Organizations

University of Trento
Italy
University of Modena and Reggio Emilia
Italy

Keywords

regularity, Caccioppoli partitions, Variational problems in a geometric measure-theoretic setting, Regularity of solutions in optimal control, variational image segmentation, Caccioppoli partitions; generalised mean curvature, prescribed mean curvature, Existence theories for free problems in two or more independent variables

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