Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem

Adrian I. Nachman
Annals of Mathematics
Second Series, Vol. 143, No. 1 (Jan., 1996), pp. 71-96
Published by: Annals of Mathematics
DOI: 10.2307/2118653
Stable URL: http://www.jstor.org/stable/2118653
Page Count: 26
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem
Preview not available

Abstract

We show that the coefficient γ(x) of the elliptic equation ∇ · (γ ∇ u) = 0 in a two-dimensional domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the boundary, and give a reconstruction procedure. For the equation Σ ∂i (γij ∂j u) = 0, two matrix-valued functions γ1 and γ2 yield the same Dirichlet-to-Neumann map if and only if there is a diffeomorphism of the domain which fixes the boundary and transforms γ1 into γ2.

Page Thumbnails

  • Thumbnail: Page 
[71]
    [71]
  • Thumbnail: Page 
72
    72
  • Thumbnail: Page 
73
    73
  • Thumbnail: Page 
74
    74
  • Thumbnail: Page 
75
    75
  • Thumbnail: Page 
76
    76
  • Thumbnail: Page 
77
    77
  • Thumbnail: Page 
78
    78
  • Thumbnail: Page 
79
    79
  • Thumbnail: Page 
80
    80
  • Thumbnail: Page 
81
    81
  • Thumbnail: Page 
82
    82
  • Thumbnail: Page 
83
    83
  • Thumbnail: Page 
84
    84
  • Thumbnail: Page 
85
    85
  • Thumbnail: Page 
86
    86
  • Thumbnail: Page 
87
    87
  • Thumbnail: Page 
88
    88
  • Thumbnail: Page 
89
    89
  • Thumbnail: Page 
90
    90
  • Thumbnail: Page 
91
    91
  • Thumbnail: Page 
92
    92
  • Thumbnail: Page 
93
    93
  • Thumbnail: Page 
94
    94
  • Thumbnail: Page 
95
    95
  • Thumbnail: Page 
96
    96