arXiv subjects

Oleg Yu. Imanuvilov

Publications and source records attributed to Oleg Yu. Imanuvilov.

3 recordsLinked to original sources

arXiv2020

Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

For an initial-boundary value problem for a parabolic equation in the spatial variable $x=(x_1,.., x_n)$ and time $t$, we consider an inverse problem of determining a coefficient which is independent of one spatial component $x_n$ by extra lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also we prove similar results for the corresponding inverse source problem.

math.AP↗

arXiv2012

Inverse boundary value problem for linear Schrödinger equation in two dimensions

We relax the regularity condition on potentials of Schrödinger equations in the uniqueness results in \cite{EB} and \cite{IY2} for the inverse boundary value problem of determining a potential by Dirichlet-to-Neumann map.

math-ph↗

arXiv2008

Partial Data for the Calderon Problem in Two Dimensions

We show in two dimensions that measuring Dirichlet data for the conductivity equation on an open subset of the boundary and, roughly speaking, Neumann data in slightly larger set than the complement uniquely determines the conductivity on a simply connected domain. The proof is reduced to show a similar result for the Schrödinger equation. Using Carleman estimates with degenerate weights we construct appropriate complex geometrical optics solutions to prove the results.

math.AP↗