Two-Point Boundary Value Problems on Diffeomorphism Groups
Differential Geometry
2022-06-22 v2 Analysis of PDEs
Abstract
We consider a variety of geodesic equations on Sobolev diffeomorphism groups, including the equations of ideal hydrodynamics. We prove that solutions of the corresponding two-point boundary value problems are precisely as smooth as their boundary conditions. We further utilise this regularity property to construct continuously differentiable exponential maps in the Frech\'et setting.
Cite
@article{arxiv.2110.12278,
title = {Two-Point Boundary Value Problems on Diffeomorphism Groups},
author = {Patrick Heslin},
journal= {arXiv preprint arXiv:2110.12278},
year = {2022}
}
Comments
18 pages