80 research outputs found
Stability of the unique continuation for the wave operator via Tataru inequality and applications
In this paper we study the stability of the unique continuation in the case
of the wave equation with variable coefficients independent of time. We prove a
logarithmic estimate in a arbitrary domain of , where all
the parameters are calculated explicitly in terms of the -norm of the
coefficients and on the other geometric properties of the problem. We use the
Carleman-type estimate proved by Tataru in 1995 and an iteration for locals
stability. We apply the result to the case of a wave equation with data on a
cylinder an we get a stable estimate for any positive time, also after the
first conjugate point for the geodesics of the metric related to the variable
coefficients.Comment: The version v1 of this preprint is an extended version that contains
more details than the "journal version", that is, the version v2, of the
pape
Spectral theory and inverse problem on asymptotically hyperbolic orbifolds
We consider an inverse problem associated with -dimensional asymptotically
hyperbolic orbifolds having a finite number of cusps and regular
ends. By observing solutions of the Helmholtz equation at the cusp, we
introduce a generalized -matrix, and then show that it determines the
manifolds with its Riemannian metric and the orbifold structure
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