Stability of the inverse problem in potential scattering at fixed energy

Plamen Stefanov

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 4, page 867-884
  • ISSN: 0373-0956

Abstract

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We prove an estimate of the kind ∥ q 1 - q 2 ∥ L ∞ ≤ C ϕ ( ∥ A q 1 - A q 2 ∥ R , 3 / 2 - 1 / 2 ) , where A q i ( ω , θ ) , i = 1 , 2 is the scattering amplitude related to the compactly supported potential q i ( x ) at a fixed energy level k = const., ϕ ( t ) = ( - ln t ) - δ , 0 < δ < 1 and ∥ · ∥ R , 3 / 2 - 1 / 2 is a suitably defined norm.

How to cite

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Stefanov, Plamen. "Stability of the inverse problem in potential scattering at fixed energy." Annales de l'institut Fourier 40.4 (1990): 867-884. <http://eudml.org/doc/74903>.

@article{Stefanov1990,
abstract = {We prove an estimate of the kind $\Vert q_1-q_2\Vert _\{L^\infty \} \le C \phi (\Vert A_\{q_1\}-A_\{q_2\}\Vert _\{R,3/2-1/2\})$, where $A_\{q_i\}(\omega ,\theta )$, $i=1,2$ is the scattering amplitude related to the compactly supported potential $q_i(x)$ at a fixed energy level $k=$ const., $\phi (t) = (-\ln t)^\{-\delta \}$, $0&lt; \delta &lt; 1$ and $\Vert \cdot \Vert _\{R,3/2-1/2\}$ is a suitably defined norm.},
author = {Stefanov, Plamen},
journal = {Annales de l'institut Fourier},
keywords = {stability estimate; unknown potential},
language = {eng},
number = {4},
pages = {867-884},
publisher = {Association des Annales de l'Institut Fourier},
title = {Stability of the inverse problem in potential scattering at fixed energy},
url = {http://eudml.org/doc/74903},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Stefanov, Plamen
TI - Stability of the inverse problem in potential scattering at fixed energy
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 4
SP - 867
EP - 884
AB - We prove an estimate of the kind $\Vert q_1-q_2\Vert _{L^\infty } \le C \phi (\Vert A_{q_1}-A_{q_2}\Vert _{R,3/2-1/2})$, where $A_{q_i}(\omega ,\theta )$, $i=1,2$ is the scattering amplitude related to the compactly supported potential $q_i(x)$ at a fixed energy level $k=$ const., $\phi (t) = (-\ln t)^{-\delta }$, $0&lt; \delta &lt; 1$ and $\Vert \cdot \Vert _{R,3/2-1/2}$ is a suitably defined norm.
LA - eng
KW - stability estimate; unknown potential
UR - http://eudml.org/doc/74903
ER -

References

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  14. [SU3] J. SYLVESTER and G. UHLMANN, Inverse boundary value problem at the boundary - continuous dependence, Comm. Pure Appl. Math., 41 (1988), 197-221. Zbl0632.35074MR89f:35213
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