Group Seminar: Inverse Problems and Mathematical Imaging
Group Seminar via Zoom
Title: Stability estimates for some anisotropic inverse problems
Time: Oct. 4, 2023, 14:30
Zoom Meeting:
https://univienna.zoom.us/j/64894413255?pwd=T3A2ZUJrNUJpeEpVd1VCalUzSEU2dz09
The stability analysis of an inverse problem is a fundamental step that may
support the corresponding reconstruction procedure. In this talk, we review
two recent results concerning the stability issue for the inverse boundary value
problem associated with the generalised Schr¨odinger type equation
div(σ∇u) + q u = 0 in Ω , (1)
where σ is a real n × n symmetric L∞ matrix function and q is a measurable
bounded scalar function. First, we consider the inclusion determination problem
and we derive a log-type stability estimate for the Hausdorff distance between
the closure of the two inclusions in terms of the local Cauchy data, which models
the known boundary measurements. This is based on a joint work with Eva
Sincich. Then, we consider the inverse problem of the simultaneous identification
of two coefficients and we derive a Lipschitz stability estimate in terms of
the local Cauchy data.