"Spectral Theory and Mathematical Physics"
In honor of Vladimir Georgescu
Cergy-Pontoise, June 21-24, 2016.
Photo Credit: Cergy - Axe majeur,
www.cergypontoise.fr/jcms/p2_85721/fr/le-patrimoine-moderne
| Program Spyros Alexakis Kaïs Ammari Jean-Marc Bouclet Jan Derezinski Clotilde Fermanian Kammerer Christian Gérard Sylvain Golénia Dietrich Häfner Matti Lassas Mathieu Lewin Jacob Schach Moller Francis Nier Victor Nistor Benoit Pausader Main page |
Matti Lassas: Scattering in complex geometrical optics and the inverse problem for the conductivity equation Abstract: We study Calderon's inverse problem in the two-dimensional case, that is, the question whether the properties of the conductivity function inside a domain can be determined from the voltage and current measurements made on the boundary. We determine the locations of the jumps of the conductivity function. To do this, we introduce a new method based on the propagation of singularities and the scattering of the singularities from the discontinuities of the coefficient functions. While the conductivity equation satisfied by an electrostatic field is an elliptic equation and does not propagate singularities, the associated equations which are used to construct so-called complex geometrical optics (CGO) solutions are of complex principal type. Standard hyperbolic wave equations satisfied by, e.g., acoustic waves, are examples of real principal type equations, which efficiently propagate singularities along one-dimensional characteristics, that is, along rays. Complex principal type equations propagate singularities along two-dimensional bicharacteristic leaves. In the talk we consider the propagation and scattering of these singularities. This is joint work with A. Greenleaf, M. Santacesaria, S. Siltanen and G. Uhlmann. |
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