Team, Visitors, External Collaborators
Overall Objectives
Research Program
New Software and Platforms
New Results
Partnerships and Cooperations
XML PDF e-pub
PDF e-Pub

Section: New Results

Metric completion of Diff ([0,1]) with the right-invariant H1 metric

S. di Marino, A. Natale, R. Tahraoui, F-X. Vialard. In [21]: We consider the group of smooth increasing diffeomorphisms Diff on the unit interval endowed with the right-invariant H1 metric. We compute the metric completion of this space which appears to be the space of increasing maps of the unit interval with boundary conditions at 0 and 1. We compute the lower-semicontinuous envelope associated with the length minimizing geodesic variational problem. We discuss the Eulerian and Lagrangian formulation of this relaxation and we show that smooth solutions of the EPDiff equation are length minimizing for short times.