Titel
Fractional Sobolev metrics on spaces of immersions
Autor*in
Martin Bauer
Faculty for Mathematics, Florida State University
Philipp Harms
Freiburg Institute of Advanced Studies, Faculty for Mathematics, Freiburg University
Abstract
We 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.
Stichwort
Applied MathematicsAnalysis
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Calculus of Variations and Partial Differential Equations
Band
59
Ausgabe
2
ISSN
0944-2669
Erscheinungsdatum
2020
Publication
Springer Science and Business Media LLC
Erscheinungsdatum
2020
Zugänglichkeit
Rechte
Rechteangabe
© The Author(s) 2020
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