1,721,002 research outputs found
Remark on the strong unique continuation property for parabolic operators
No full textWe consider solutions , in a neighbourhood of , to a parabolic differential equation with variable coefficients depending on space and time variables. We assume that the coefficients in the principal part are Lipschitz continuous and that those in the lower order terms are bounded. We prove that, if vanishes of infinite order at , then
Lipschitz Stability for the Inverse Conductivity Problem
No full textWe discuss the stability issue for Calderón's inverse conductivity problem, also known as Electrical Impedance Tomography. It is well known that this problem is severely ill-posed. In this paper we prove that if it is a-priori known that the conductivity is piecewise constant with a bounded number of unknown values, then a Lipschitz stability estimate holds
A stability result in the localization of cavities in a thermic conducting medium
No full textWe prove a logarithmic stability estimate for a parabolic inverse problem concerning the
localization of unknown cavities in a thermic conducting medium
in Rn, n 2, from a single pair of
boundary measurements of temperature and thermal flux
Quantitative estimates of unique continuation for parabolic equations and inverse initial-boundary value problemswith unknown boundaries
No full textIn this paper we obtain quantitative estimates of strong unique continuation for solutions to parabolic equations. We apply these results to prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain Omega in R(n), from the knowledge of overdetermined boundary data for parabolic boundary value problems
Detecting general inclusions in elastic plates
No full textWe consider the problem of
determining, within an elastic isotropic thin plate, the possible
presence of an inclusion made of different elastic material. We
prove constructive upper and lower estimates of the area of the
inclusion in terms of the work exerted by a couple field applied
at the boundary and of the induced transversal displacement and
its normal derivative taken at the boundary of the plate
Stable determination of a rigid inclusion in an anisotropic plate
No full textIn this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement
and its normal derivative at the boundary of the plate. The plate is made by non-homogeneous linearly elastic material belonging to
a general class of anisotropy. For this severely ill-posed
problem, under suitable a priori regularity assumptions on the boundary of the inclusion, we prove a stability estimate of
log-log type
The stability for the Cauchy problem for elliptic equations
No full textWe discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality
A parabolic inverse problem with mixed boundary data. Stability estimates for the unknown boundary and impedance
No full textWe consider the problem of determining an unaccessible part of
the boundary of a conductor by mean of thermal measurements. We study a
problem of corrosion where a Robin type condition is prescribed on the damaged
part and we prove logarithmic stability estimate
- …
