Institut Henri Poincaré (IHP)
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THE CALDERON PROBLEM IN TRANSVERSALLY ANISOTROPIC GEOMETRIES
We consider the anisotropic Calderón problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work , it was shown that a metric in a fixed conformal class is uniquely deter-mined by boundary measurements under two conditions: (1) the metric is conform...
Null-controllability of the Kolmogorov equation in the whole phase space
Null-controllability of the Kolmogorov equation in the whole phase space. 2014. HAL Id: hal-01134917 https://hal.archives-ouvertes.fr/hal-01134917v2 Submitted on 2 Apr 2015 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come ...
STABILITY ESTIMATES FOR THE RADON TRANSFORM WITH RESTRICTED DATA AND APPLICATIONS
In this article, we prove a stability estimate going from the Radon transform of a function with limited angle-distance data to the L p norm of the function itself, under some conditions on the support of the function. We apply this theorem to obtain stability estimates for an inverse boundary value problem with partial data.
INVARIANT DISTRIBUTIONS AND X-RAY TRANSFORM FOR ANOSOV FLOWS
For Anosov flows preserving a smooth measure on a closed manifold M, we define a natural self-adjoint operator Π which maps into the space of in-variant distributions in ∩ u<0 H u (M) and whose kernel is made of coboundaries in ∪ s>0 H s (M). We describe relations to Livsic theorem and recover regularity proper-ties of cohomological equations using...
INVERSE PROBLEMS IN SPACETIME I: INVERSE PROBLEMS FOR EINSTEIN EQUATIONS
We consider inverse problems for the coupled Einstein equations and the matter field equations on a 4-dimensional globally hyperbolic Lorentzian manifold (M, g). We give a positive answer to the question: Do the active measurements, done in a neighborhood U ⊂ M of a freely falling observed µ = µ([s − , s + ]), determine the conformal structure of t...
On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients
Published in Journal of Applied Mathematics
We investigate a level-set-type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem, we propose a Tikhonov-type regularization approach coupled with a l...
Flowability of plane homeomorphisms
Published in Annales de l’institut Fourier
We describe necessary and sufficient conditions for a fixed point free planar homeomorphism that preserves the standard Reeb foliation to embed in a planar flow that leaves the foliation invariant.