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Inversion Formulas arising in Inverse Boundary Value Problems

Inversion Formulas arising in Inverse Boundary Value Problems
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Inverse boundary value problems with unknown boundaries: Optimal stability

Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics, 2000
Summary: 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, BERETTA E, ROSSET, EDI, VESSELLA S.   +3 more
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Inverse boundary value problems at the boundary—continuous dependence

Communications on Pure and Applied Mathematics, 1988
AbstractWe 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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Boundary value method for inverse Sturm–Liouville problems

Applied Mathematics and Computation, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kammanee, Athassawat, Böckmann, Christine   +1 more
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An Inverse Boundary Value Problem in Seismology

Physics, 1934
It 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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An Inverse Boundary Value Problem in Electrodynamics

Physics, 1933
From 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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Inverse Boundary Value Problems

1999
In this book, so far, we have considered only so-called direct boundary value problems where, given a differential equation, its domain, and a boundary condition, we want to determine its solution.
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Multi-Dimensional Inverse Boundary Value Problems

2020
The inverse spectral problem for boundary value problem of differential operators has been raised and studied from various viewpoints. We recall some of the sources of the problem in this chapter.
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