Approximation of the elastic Dirichlet-to-Neumann map

DOI10.3934/IPI.2022042arXiv2201.04825MaRDI QIDQ6388155

Georgi Vodev

Publication date: 13 January 2022

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.

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Inverse problems for PDEs (35R30) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Boundary value problems for second-order elliptic systems (35J57)

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