Topological derivative of domain dependent functionals

Inverse Problems and Applications

11 February 15:30 - 16:30


Consider the following inverse problem. We have a domain and an operator associated with it and as a result we have also eigenvalues and eigenfunctions of this operator. Then the domain is changed because of appearance of holes, various defects, boundary erosion, part of the domain may take another properties and so on. Our goal is determine these changes by changes in eigenvalues and eigenfunctions. In this connection it is useful to have an asymptotic formulae for eigenvalues and eigenfunctions which are applicable to such type of perturbations. In my lecture I am going to discuss two questions concerning this: how to measure smallness of perturbations when the topology is changed and how a general asymptotic formula looks like for such perturbations.