Going beyond variation of sets

Chlebík, Miroslav (2017) Going beyond variation of sets. Nonlinear Analysis: Theory, Methods and Applications, 153. pp. 230-242. ISSN 0362-546X

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Abstract

We study integralgeometric representations of variations of general sets A ⊂ Rn without any regularity assumptions. If we assume, for example, that just one partial derivative of its characteristic function χA is a signed Borel measure on R n with finite total variation, can we provide a nice integralgeometric representation of this variation? This is a delicate question, as the Gauss-Green type theorems of De Giorgi and Federer are not available in this generality. We will show that a ‘measure-theoretic boundary’ plays its role in such representations similarly as for the sets of finite variation. There is a variety of suitable notions of ‘measure theoretic boundary’ and one can address the question to find notions of measure-theoretic boundary that are as fine as possible.

Item Type: Article
Keywords: perimeter of sets, measure-theoretic boundary, integral geometric measure
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Miroslav Chlebik
Date Deposited: 18 Nov 2016 09:17
Last Modified: 21 Apr 2017 12:37
URI: http://sro.sussex.ac.uk/id/eprint/65519

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