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)
|Martin Bauer||Florida State University|
|Philipp Harms||Nanyang Technological University Singapore|
|Peter Michor||University of Vienna|