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Regularity of almost minimizing sets / Regularidade dos conjuntos quase minimizantes

This work was motivated by the famous Plateau\'s Problem which concerns the existence of a minimizing set of the area functional with prescribed boundary. In order to solve the Plateau\'s Problem, we make use of different theories: the theory of varifolds, currents and locally finite perimeter sets (Caccioppoli sets). Working on the Caccioppoli sets theory, it is straightforward to prove the existence of a minimizing set in some classical problems as the isoperimetric and Plateau\'s problems. If we switch the problem to find the regularity that we can extract of some minimizing set, we come across complicated ideas and tools. Although, the Plateau\'s Problem and other classical problems are well settled. Because of that, we have extensively studied the almost minimizing condition ((; r)-minimizing sets) considered by Maggi ([?]) which subsumes some classical problems. We focused on the regularity theory extracted from this almost minimizing condition. / This work was motivated by the famous Plateau\'s Problem which concerns the existence of a minimizing set of the area functional with prescribed boundary. In order to solve the Plateau\'s Problem, we make use of different theories: the theory of varifolds, currents and locally finite perimeter sets (Caccioppoli sets). Working on the Caccioppoli sets theory, it is straightforward to prove the existence of a minimizing set in some classical problems as the isoperimetric and Plateau\'s problems. If we switch the problem to find the regularity that we can extract of some minimizing set, we come across complicated ideas and tools. Although, the Plateau\'s Problem and other classical problems are well settled. Because of that, we have extensively studied the almost minimizing condition ((; r)-minimizing sets) considered by Maggi ([?]) which subsumes some classical problems. We focused on the regularity theory extracted from this almost minimizing condition.

Identiferoai:union.ndltd.org:usp.br/oai:teses.usp.br:tde-28082019-125158
Date31 July 2019
CreatorsOliveira, Reinaldo Resende de
ContributorsNardulli, Stefano, Terra, Glaucio
PublisherBiblioteca Digitais de Teses e Dissertações da USP
Source SetsUniversidade de São Paulo
LanguageEnglish
Detected LanguageEnglish
TypeDissertação de Mestrado
Formatapplication/pdf
RightsLiberar o conteúdo para acesso público.

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