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arXiv · 2110.12278

Two-Point Boundary Value Problems on Diffeomorphism Groups

Patrick Heslin
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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.

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Patrick Heslin. 2021-10-23. Two-Point Boundary Value Problems on Diffeomorphism Groups. https://arxiv.org/abs/2110.12278

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