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Inverse problems for elliptic PDEs, analysis and applications

Organizers:
Laurent Baratchart and Juliette Leblond, INRIA Sophia Antipolis, team Apics

Abstract:
The present minisymposium concerns inverse potential and geometric problems, from overdetermined boundary data or from farfield patterns, for elliptic (conductivity or Schrdinger type) PDEs in dimensions 2 and 3. A first group of three talks (by Bonnetier, Bourgeois, Sincich) is concerned with conductivity equations and the inverse problems of computing either this conductivity or unknown boundary conditions (Robin coefficients), from incomplete overdetermined boundary data or/and energy amplitude estimates. Uniqueness and stability issues are considered. A second group of two talks (Haddar, Zagrebnov) is concerned with inverse free boundary value problems. Geometric techniques from Laplacian transport are used to determine shapes from boundary data, while linear sampling methods are used to locate defaults for the Helmholtz equation, and applied to non destructive testing. A third group of two talks (Chevillard, Ponomarev) deals with inverse potential problems with known support and density in divergence form, which can be viewed as recovering Cauchy data from interior values of solutions to Poisson-Laplace equation. Applications to paleomagnetism are mentionned. Finally, one of the talks (Novikov) is concerned with inverse scattering, where the potential in a 3D Schrdinger equation is to be recovered from the scattering amplitude at a fixed energy level. The scattering amplitude is given on some 3-dimensional hypersurface of the domain of definition.