On the planar minimal BV extension problem
Aldo Pratelli
Universität Erlangen-Nürnberg, GermanyEmanuela Radici
Università degli Studi dell'Aquila, Italy
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Abstract
Given a continuous, injective function defined on the boundary of a planar open set , we consider the problem of minimizing the total variation among all the BV homeomorphisms on coinciding with on the boundary. We find the explicit value of this infimum in the model case when is a rectangle. We also present two important consequences of this result: first, whatever the domain is, the infimum above remains the same also if one restricts himself to consider only homeomorphisms. Second, any BV homeomorphism can be approximated in the strict BV sense with piecewise affine homeomorphisms and with diffeomorphisms.
Cite this article
Aldo Pratelli, Emanuela Radici, On the planar minimal BV extension problem. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 3, pp. 511–555
DOI 10.4171/RLM/819