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Two-Point Boundary Value Problems on Diffeomorphism Groups (2110.12278v2)
Published 23 Oct 2021 in math.DG and math.AP
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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