Displaying similar documents to “Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions”

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

David Krejčiřík (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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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 Dirichlet...

Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions

David Krejčiřík (2014)

Mathematica Bohemica

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We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the hypersurfaces 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 area...

30 Years of Calderón’s Problem

Gunther Uhlmann (2012-2013)

Séminaire Laurent Schwartz — EDP et applications

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In this article we survey some of the most important developments since the 1980 paper of A.P. Calderón in which he proposed the problem of determining the conductivity of a medium by making voltage and current measurements at the boundary.

Nonlinear boundary value problems for ordinary differential equations

Andrzej Granas, Ronald Guenther, John Lee

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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...