Reconstructions from boundary measurements

Soit Ω un domaine borne dans R n , n≥3 avec une frontiere C 1,1 . On considere l'operateur Lγ(u)=⊇•(γ⊇u) ou γ(x) est une fonction a valeur reelle dans C 1,1 (Ω) avec une borne superieure positive. On definit la forme quadratique Qγ sur H 1/2 (∂Ω) par Qγ(f)=∫ Ω γ(x)|⊇u(x)| 2 dx ou u∈H 1 (Ω) est la solution unique a Lγu=0 dans Ω, u| ∂Ω =f. On etudie la reconstruction de γ a partir de Qγ

[1]  J. Sylvester,et al.  Ann-dimensional Borg-Levinson theorem , 1988 .

[2]  J. Sylvester,et al.  Inverse boundary value problems at the boundary—continuous dependence , 1988 .

[3]  R. Novikov,et al.  A multidimensional inverse problem in quantum and acoustic scattering , 1988 .

[4]  Giovanni Alessandrini,et al.  Stable determination of conductivity by boundary measurements , 1988 .

[5]  R G Novikov,et al.  The $ \bar\partial$-equation in the multidimensional inverse scattering problem , 1987 .

[6]  J. Sylvester,et al.  A global uniqueness theorem for an inverse boundary value problem , 1987 .

[7]  John Sylvester,et al.  A uniqueness theorem for an inverse boundary value problem in electrical prospection , 1986 .

[8]  R. Kohn,et al.  Determining conductivity by boundary measurements II. Interior results , 1985 .

[9]  P. Grisvard.  Elliptic Problems in Nonsmooth Domains , 1985 .

[10]  Mark J. Ablowitz,et al.  A Multidimensional Inverse-Scattering Method , 1984 .

[11]  G. Verchota.  Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains , 1984 .

[12]  M. Cheney,et al.  Velocity and Density of a Two-Dimensional Acoustic Medium from Point Source Surface Data, , 1984 .

[13]  Robert V. Kohn,et al.  Determining conductivity by boundary measurements , 1984 .

[14]  G Beylkin,et al.  Diffraction tomography using arbitrary transmitter and receiver surfaces. , 1984, Ultrasonic imaging.

[15]  R. Kress,et al.  Integral equation methods in scattering theory , 1983 .

[16]  R. Lavine.  Classical Limit of the Number of Quantum States , 1981 .

[17]  J. Jodeit,et al.  Potential techniques for boundary value problems on C1-domains , 1978 .

[18]  Shmuel Agmon,et al.  Spectral properties of Schrödinger operators and scattering theory , 1975 .

[19]  Mark S. C. Reed,et al.  Method of Modern Mathematical Physics , 1972 .