English

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.

Keywords

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

R2 v1 2026-06-24T07:07:46.833Z