Author:
Bauer Martin,Harms Philipp,Michor Peter W.
Abstract
AbstractWe prove that the geodesic equations of all Sobolev metrics of fractional order one and higher on spaces of diffeomorphisms and, more generally, immersions are locally well posed. This result builds on the recently established real analytic dependence of fractional Laplacians on the underlying Riemannian metric. It extends several previous results and applies to a wide range of variational partial differential equations, including the well-known Euler–Arnold equations on diffeomorphism groups as well as the geodesic equations on spaces of manifold-valued curves and surfaces.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Cited by
6 articles.
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