Manifolds of mappings for continuum mechanics
Differential Geometry
2021-11-02 v3 Analysis of PDEs
Abstract
This is an overview article. After an introduction to convenient calculus in infinite dimensions, the foundational material for manifolds of mappings is presented. The central character is the smooth convenient manifold of all smooth mappings from a finite dimensional Whitney manifold germ into a smooth manifold . A Whitney manifold germ is a smooth (in the interior) manifold with a very general boundary, but still admitting a continuous Whitney extension operator. This notion is developed here for the needs of geometric continuum mechanics.
Keywords
Cite
@article{arxiv.1909.00445,
title = {Manifolds of mappings for continuum mechanics},
author = {Peter W. Michor},
journal= {arXiv preprint arXiv:1909.00445},
year = {2021}
}
Comments
66 pages. arXiv admin note: substantial text overlap with arXiv:1505.02359, arXiv:math/9202208. Last version: some misprintscorrected