Publications
2015
Issue 34

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

34/2015

Residually many BV homeomorphisms map a null set in a set of full measure

Andrea Marchese

Abstract

Let $Q = [0, 1]^{2}$ be the unit square in $R^{2}$ . We prove that in a suitable complete metric space of $B V$ homeomorphisms $f : Q \to Q$ with $f_{| \partial Q} = I d$ , the generical homeomorphism (in the sense of Baire categories) maps a null set in a set of full measure and vice versa. Moreover we observe that, for $1 \leq p < 2$ , in the most reasonable complete metric space for such problem, the family of $W^{1, p}$ homemomorphisms satisfying the above property is of first category, instead.

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Received:: 03.06.15

Published:: 04.06.15

MSC Codes:: 46B35, 26B35

Keywords:: Sobolev homeomorphism, baire categories, piecewise affine homeomorphism

Related publications

inJournal

2019 Repository Open Access

Andrea Marchese

Residually many BV homeomorphisms map a null set onto a set of full measure

In: Proceedings of the Royal Society of Edinburgh / A, 149 (2019) 4, pp. 1047-1059

BibTex DOI: 10.1017/prm.2018.104 ArXiv: 1506.01234