51 research outputs found
Smoothness dependent stability in corrosion detection
We consider the stability issue for the determination of a linear corrosion
in a conductor by a single electrostatic measurement. We established a global
log-log type stability when the corroded boundary is simply Lipschitz. We also
improve such a result obtaining a global log stability by assuming that the
damaged boundary is -smooth
Stable determination of the surface impedance of an obstacle by far field measurements
We deal with the inverse scattering problem of determining the surface
impedance of a partially coated obstacle. We prove a stability estimate of
logarithmic type for the impedance term by the far field measurements
Stability for the determination of unknown boundary and impedance with a Robin boundary condition
We consider an inverse problem arising in corrosion detection. We prove a
stability result of logarithmic type for the determination of the corroded
portion of the boundary and impedance by two measurements on the accessible
portion of the boundary
Wave equation with Robin condition, quantitative estimates of strong unique continuation at the boundary
The main result of the present paper consists in a quantitative estimate of
unique continuation at the boundary for solutions to the wave equation. Such
estimate is the sharp quantitative counterpart of the following strong unique
continuation property: let be a solution to the wave equation that
satisfies an homogeneous Robin condition on a portion of the boundary and
the restriction of on is flat on a segment
with then vanishes in a neighborhood of
Cracks with impedance, stable determination from boundary data
We discuss the inverse problem of determining the possible presence of an
(n-1)-dimensional crack \Sigma in an n-dimensional body \Omega with n > 2 when
the so-called Dirichlet-to-Neumann map is given on the boundary of \Omega. In
combination with quantitative unique continuation techniques, an optimal
single-logarithm stability estimate is proven by using the singular solutions
method. Our arguments also apply when the Neumann-to-Dirichlet map or the local
versions of the D-N and the N-D map are available.Comment: 40 pages, submitte
Stability and reconstruction for the determination of boundary terms by a single measurement
In this thesis we treat two inverse problems concerning the determination of unknown boundary terms. We deal with the stability issue and the reconstruction one as well
Stable determination of an anisotropic inclusion in the Schr\"odinger equation from local Cauchy data
We consider the inverse problem of determining an inclusion contained in a
body for a Schr\"odinger type equation by means of local Cauchy data. Both the
body and the inclusion are made by inhomogeneous and anisotropic materials.
Under mild a priori assumptions on the unknown inclusion, we establish a
logarithmic stability estimate in terms of the local Cauchy data. In view of
possible applications, we also provide a stability estimate in terms of an
ad-hoc misfit functional.Comment: pp. 3
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