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A global uniqueness theorem for an inverse boundary value problem
In this paper, we show that the single smooth coefficient of the elliptic operator LY = v yv can be determined from knowledge of its Dirichlet integrals for arbitrary boundary values on a fixedExpand
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Corners Always Scatter
We study time harmonic scattering for the Helmholtz equation in $${\mathbb{R}^n}$$Rn. We show that certain penetrable scatterers with rectangular corners scatter every incident wave nontrivially.Expand
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Discreteness of Transmission Eigenvalues via Upper Triangular Compact Operators
  • J. Sylvester
  • Mathematics, Computer Science
  • SIAM J. Math. Anal.
  • 21 April 2011
TLDR
Transmission eigenvalues are points in the spectrum of the interior transmission operator, a coupled $2 \times 2$ system of elliptic partial differential equations where one unknown function must satisfy two boundary conditions and the other must satisfy none. Expand
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A uniqueness theorem for an inverse boundary value problem in electrical prospection
We show that a near constant conductivity of a two-dimensional body can be uniquely determined by steady state direct current measurements at the boundary. Mathematically, we show that theExpand
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The interior transmission problem
The interior transmission problem is a boundary value problem that plays a basic role in inverse scattering theory but unfortunately does not seem to be included in any existing theory in partialExpand
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The scattering support
We discuss inverse problems for the Helmholtz equation at fixed energy, specifically the inverse source problem and the inverse scattering problem from a medium or an obstacle. We introduce theExpand
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The heat equation and reflected Brownian motion in time-dependent domains
The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as "noncylindrical domains,'' and its connections with partial differentialExpand
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An anisotropic inverse boundary value problem
We consider the impedance tomography problem for anisotropic conductivities. Given a bounded region Ω in space, a diffeomorphism Ψ from Ω to itself which restricts to the identity on ∂ Ω, and aExpand
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A 'range test' for determining scatterers with unknown physical properties
We describe a new scheme for determining the convex scattering support of an unknown scatterer when the physical properties of the scatterers are not known. The convex scattering support is a subsetExpand
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Inverse boundary value problems at the boundary—continuous dependence
We 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 voltageExpand
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