GRADIENT FLOW FOR KOHN-VOGELIUS FUNCTIONAL

Аннотация

The identification problem of an inclusion is considered
in the paper. The inclusion is unknown subdomain of a given physical
region. The available information on the inclusion is governed by measurements
on the boundary of this region. In particular, the single measurement
problem of impedance electrotomography and similar inverse problems
are included in our approach. The shape identification problem can be
solved by the minimization of an objective function taking into account
the measurement data. The best choice of such objective function is
the Kohn-Vogelius energy functional. The standard regularization of the
Kohn-Vogelius functional include the perimeter and Willmore curvature
functional evaluated for an admissible inclusion boundary. In the twodimensional case, a nonlocal existence theorem of strong solutions is
proved for the gradient flow dynamical system generated for such a
regularization of the Kohn-Vogelius functional. Bibliography: 14 titles.