Research in Teams Project: Geodesic Equations on Mapping Spaces

Research Project:

A successful strategy, due to Ebin and Marsden (1970), for establishing well-posedness of variational PDEs is to prove that the Euler-Lagrange equations extend to smooth vector fields on Sobolev completions of the configuration space. This typically means verifying that certain partial or pseudo differential operators depend smoothly on their coefficients in suitable Sobolev topologies. The goal of this project is to study this question in the context of fractional powers (or more general functions) of Laplacians which are defined with respect to Riemannian metrics of finite Sobolev regularity. This research has applications in shape analysis and mathematical hydrodynamics.

Research Team: Martin Bauer (Florida State U), Philipp Harms (U Freiburg), Peter W. Michor (U Vienna)

Coming soon.


Name Affiliation
Martin Bauer Florida State University
Philipp Harms Nanyang Technological University Singapore
Peter Michor University of Vienna
At a glance
Research in Teams
June 17, 2019 — July 31, 2019
Erwin Schrödinger Institute