Boundary determination of the Riemannian metric by the elastic Dirichlet-to-Neumann map

TL;DR

This paper proves that the elastic Dirichlet-to-Neumann map uniquely determines all boundary derivatives of the Riemannian metric on a compact manifold, advancing inverse boundary value problem understanding.

Contribution

It establishes the boundary determination of the Riemannian metric's derivatives from the elastic Dirichlet-to-Neumann map, a novel result in inverse problems for elastic manifolds.

Findings

Unique determination of boundary derivatives of the metric

Full symbol computation of the elastic Dirichlet-to-Neumann map

Advancement in inverse boundary value problems for elastic manifolds

Abstract

For a compact connected Riemannian manifold with smooth boundary, by computing the full symbol of the elastic Dirichlet-to-Neumann map, we prove that the elastic Dirichlet-to-Neumann map can uniquely determine the partial derivatives of all orders of the Riemannian metric on the boundary of the manifold.