APPROXIMATION OF THE ELASTIC DIRICHLET-TO-NEUMANN MAP

被引：1
|
作者：
Vodev, Georgi [1 ]
机构：
[1] Univ Nantes, Lab Math Jean Leray, 2 Rue Houssiniere,BP 92208, F-44322 Nantes 03, France
来源：
INVERSE PROBLEMS AND IMAGING | 2023年 / 17卷 / 01期
关键词：
Linear equation of elasticity; Dirichlet-to-Neumann map; LINEAR ELASTICITY; RESONANCES;
D O I：
10.3934/ipi.2022042
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the Dirichlet-to-Neumann map for the stationary linear equation of elasticity in a bounded domain in R-d, d >= 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.
引用
收藏
页码：297 / 318
页数：22
相关论文
共 50 条
  • [1] On the local Dirichlet-to-Neumann map
    Uhlmann, G
    [J]. NEW ANALYTIC AND GEOMETRIC METHODS IN INVERSE PROBLEMS, 2004, : 261 - 279
  • [2] Dirichlet-to-Neumann map for three-dimensional elastic waves
    Gächter, GK
    Grote, MJ
    [J]. WAVE MOTION, 2003, 37 (03) : 293 - 311
  • [3] The scattering relation and the Dirichlet-to-Neumann map
    Pestov, Leonid
    Uhlmann, Gunther
    [J]. RECENT ADVANCES IN DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2006, 412 : 249 - 262
  • [4] Determining Lame coefficients by the elastic Dirichlet-to-Neumann map on a Riemannian manifold
    Tan, Xiaoming
    Liu, Genqian
    [J]. INVERSE PROBLEMS, 2023, 39 (09)
  • [5] Stability of spectral partitions and the Dirichlet-to-Neumann map
    Berkolaiko, G.
    Canzani, Y.
    Cox, G.
    Marzuola, J. L.
    [J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2022, 61 (06)
  • [6] Stability of spectral partitions and the Dirichlet-to-Neumann map
    G. Berkolaiko
    Y. Canzani
    G. Cox
    J. L. Marzuola
    [J]. Calculus of Variations and Partial Differential Equations, 2022, 61
  • [7] The Determinant of the Dirichlet-to-Neumann Map for Surfaces with Boundary
    Guillarmou, Colin
    Guillope, Laurent
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2007, 2007
  • [8] The Complete Dirichlet-to-Neumann Map for Differential Forms
    Vladimir Sharafutdinov
    Clayton Shonkwiler
    [J]. Journal of Geometric Analysis, 2013, 23 : 2063 - 2080
  • [9] The boundary distance function and the Dirichlet-to-Neumann map
    Pestov, L
    Uhlmann, G
    [J]. MATHEMATICAL RESEARCH LETTERS, 2004, 11 (2-3) : 285 - 297
  • [10] The Complete Dirichlet-to-Neumann Map for Differential Forms
    Sharafutdinov, Vladimir
    Shonkwiler, Clayton
    [J]. JOURNAL OF GEOMETRIC ANALYSIS, 2013, 23 (04) : 2063 - 2080
12345