Displaying similar documents to “30 Years of Calderón’s Problem”

Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions

David Krejčiřík (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider the Laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the...

Crack detection using electrostatic measurements

Martin Brühl, Martin Hanke, Michael Pidcock (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes...

Nonlinear boundary value problems for ordinary differential equations

Andrzej Granas, Ronald Guenther, John Lee

Similarity:

CommentsThis tract is intended to be accessible to a broad spectrum of readers. Those with out much previous experience with differential equations might find it profitable (when the need arises) to consult one of the following standard texts: Coddington-Levinson [17], Hale [35], Hartman [38], Mawhin-Rouche [61]. The bibliography given below is restricted mostly to the problems discussed in the tract or closely related topics. A small number of additional references are included however...