Two-Point Boundary Value Problems on Diffeomorphism Groups

2021/10/23 by Patrick Heslin, Heslin, Patrick
Mathematics · #58D05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2110.12278

openalex publication_date 2021/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Frechét setting.

Related

• Geometric Analysis of the Generalized Surface Quasi-Geostrophic Equations
• Riemannian geometry on the quantomorphism group
• Convergence of spectral discretization for the flow of diffeomorphisms
• Curvatures of Sobolev metrics on diffeomorphism groups
• Symmetry groups of geodesic equations with applications in water waves