94 research outputs found
Tomography of small residual stresses
In this paper we study the inverse problem of determining the residual stress
in Man's model using tomographic data. Theoretically, the tomographic data is
obtained at zero approximation of geometrical optics for Man's residual stress
model. For compressional waves, the inverse problem is equivalent to the
problem of inverting the longitudinal ray transform of a symmetric tensor
field. For shear waves, the inverse problem, after the linearization, leads to
another integral geometry operator which is called the mixed ray transform.
Under some restrictions on coefficients, we are able to prove the uniqueness
results in these two cases
On the Fractional Landis Conjecture
In this paper we study a Landis-type conjecture for fractional Schr\"odinger
equations of fractional power with potentials. We discuss both the
cases of differentiable and non-differentiable potentials. On the one hand, it
turns out for \emph{differentiable} potentials with some a priori bounds, if a
solution decays at a rate , then this solution is trivial. On
the other hand, for and merely bounded \emph{non-differentiable}
potentials, if a solution decays at a rate with
, then this solution must again be trivial. Remark that when
, which is the optimal exponent for the standard
Laplacian. For the case of non-differential potentials and , we
also derive a quantitative estimate mimicking the classical result by Bourgain
and Kenig.Comment: comments are welcom
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