Boundary determination of the Riemannian metric from Cauchy data for the Stokes equations

Xiaoming Tan

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arXiv · 2408.09405

Boundary determination of the Riemannian metric from Cauchy data for the Stokes equations

Xiaoming Tan

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Abstract

For a compact connected Riemannian manifold of dimension $n$ with smooth boundary, $n\geqslant 2$, we prove that the Cauchy data (or the Dirichlet-to-Neumann map) for the Stokes equations uniquely determines the partial derivatives of all orders of the metric on the boundary of the manifold.

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Xiaoming Tan. 2024-08-18. Boundary determination of the Riemannian metric from Cauchy data for the Stokes equations. https://arxiv.org/abs/2408.09405

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