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Inversion Formulas arising in Inverse Boundary Value Problems
Inversion Formulas arising in Inverse Boundary Value Problemsopenaire
An Inverse Boundary Value Problem Arising in Nonlinear Acoustics
SIAM Journal on Mathematical Analysis, 2023 36 pages.
GÜNTHER Uhlmann
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Inverse boundary value problems at the boundary—continuous dependence
Communications on Pure and Applied Mathematics, 1988AbstractWe use the methods of microlocal analysis to give a new proof of a theorem of Kohn and Vogelius, showing that the boundary values of a continuous isotropic conductivity can be recovered from voltage and current measurements at the boundary. Moreover, we prove sharp estimates to establish the continuous dependence of the boundary values of the ...
Sylvester, John, Uhlmann, Gunther
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Inverse boundary value problems with unknown boundaries: Optimal stability
Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics, 2000Summary: We obtain essentially best possible stability estimates for a class of inverse problems associated to elliptic boundary value problems in which the role of the unknown is played by an inaccessible part of the boundary and the role of the data is played by overdetermined boundary data for the elliptic equation assigned on the remaining ...
ALESSANDRINI, GIOVANNI +3 more
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Boundary value method for inverse Sturm–Liouville problems
Applied Mathematics and Computation, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Kammanee, Christine Böckmann
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A Nonuniqueness Theorem for an Inverse Boundary Value Problem in Elasticity
SIAM Journal on Applied Mathematics, 1996Summary: The authors consider the inverse boundary value problem at the boundary for a two-dimensional anisotropic elastic medium. It is proved that the elastic tensor and its derivatives on the boundary cannot be identified from the full symbol of the Dirichlet to Neumann map.
Gen Nakamura, Kazumi Tanuma
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An Inverse Boundary Value Problem in Seismology
Physics, 1934It is shown that the variation with depth of the density and elastic constants of a half-space can be determined from the observed motion of the surface caused by a given distribution of stresses on the surface.
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Inverse Boundary Value Problem for Schrödinger Equation in Two Dimensions [PDF]
SIAM Journal on Mathematical Analysis, 2012 We relax the regularity condition on potentials of the Schrödinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].
Masahiro Yamamoto
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An Inverse Boundary Value Problem in Electrodynamics
Physics, 1933From knowledge of the electromagnetic field at the surface of a half-space due to a prescribed oscillatory source, is determined the unknown variation with depth of the conductivity and the dielectric constant. Unique solutions exist for these quantities.
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Examples of instability in inverse boundary-value problems
Inverse Problems, 1997Summary: We consider an inverse boundary-value problem arising in questions of nondestructive testing such as corrosion detection by electrostatic measurements. We construct examples which show that, for this problem, logarithmic stability is the best possible.
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