Approximation of the elastic Dirichlet-to-Neumann map

TL;DR

This paper investigates how the elastic Dirichlet-to-Neumann map can be approximated by a pseudodifferential operator with a matrix-valued symbol, providing explicit computation of its principal symbol.

Contribution

It introduces a method to approximate the elastic Dirichlet-to-Neumann map using pseudodifferential operators and calculates its principal symbol explicitly.

Findings

Approximation of the Dirichlet-to-Neumann map by a pseudodifferential operator.

Explicit computation of the principal symbol modulo unitary conjugation.

Provides a framework for analyzing elastic boundary value problems.

Abstract

We study the Dirichlet-to-Neumann map for the stationary linear equation of elasticity in a bounded domain in R d , d $\ge$ 2, with smooth boundary. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the principal symbol modulo conjugation by unitary matrices.