Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/12806
Title: Regularity of maps between sobolev spaces
Authors: Bruveris, M
Issue Date: 2016
Publisher: arXiv
Citation: arXiv, (2016)
Abstract: Let $F : H^q \to H^q$ be a $C^k$-map between Sobolev spaces, either on $\mathbb R^d$ or on a compact manifold. We show that equivariance of $F$ under the diffeomorphism group allows to trade regularity of $F$ as a nonlinear map for regularity in the image space: for $0 \leq l \leq k$, the map $F: H^{q+l} \to H^{q+l}$ is well-defined and of class $C^{k-l}$. This result is used to study the regularity of the geodesic boundary value problem for Sobolev metrics on the diffeomorphism group and the space of curves.
URI: http://arxiv.org/abs/1602.06558v1
http://bura.brunel.ac.uk/handle/2438/12806
Appears in Collections:Dept of Mathematics Research Papers

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