Given a continuous, injective function phi defined on the boundary of a planar open set Omega, we consider the problem of minimizing the total variation among all the BV homeomorphisms on Omega coinciding with phi on the boundary. We find the explicit value of this infimum in the model case when Omega is a rectangle. We also present two important consequences of this result: first, whatever the domain Omega is, the infimum above remains the same also if one restricts himself to consider only W-1,W-1 homeomorphisms. Second, any BV homeomorphism can be approximated in the strict BV sense with piecewise affine homeomorphisms and with diffeomorphisms.
Functional Analysis - On the planar minimal BV extension problem, by ALDOP RATELLI and EMANUELA RADICI, communicated on March 9, 2018
Radici, E.
2018-01-01
Abstract
Given a continuous, injective function phi defined on the boundary of a planar open set Omega, we consider the problem of minimizing the total variation among all the BV homeomorphisms on Omega coinciding with phi on the boundary. We find the explicit value of this infimum in the model case when Omega is a rectangle. We also present two important consequences of this result: first, whatever the domain Omega is, the infimum above remains the same also if one restricts himself to consider only W-1,W-1 homeomorphisms. Second, any BV homeomorphism can be approximated in the strict BV sense with piecewise affine homeomorphisms and with diffeomorphisms.Pubblicazioni consigliate
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