Elizarov A.M.  Optimal  control  of  unknown  boundary  shape  in
inverse boundary-value problems// Revue Roumaine de mathematiques
pures  et  appliquees  (Romanian  Journal  of  Pure  and  Applied
Mathematics) . -- 1995. -- V.40. -- No.2. -- P.157-168.

One of  approaches  to  optimization of unknown boundary shape is
based on  the  theory  of  inverse  boundary-value  problems  for
analytic  functions.  This  approach allows to affect actively on
characteristics  of  solutions  through  a  choice  of   boundary
conditions.

The way  developed  in  present  work  is  based  on  the idea to
describe a set of admissible solutions as an image of  the  fixed
functional  set.  Taking  into  account  conditions  of  physical
realizing (in particular,  univalence)  of  unknown  solution  we
describe  the  set of admissible functions p.  Using the set as a
set of control functions and replacing a  boundary  condition  by
the optimization requirement of a prescribed functional,  we come
to  a  variational  inverse  boundary  problem.   The   optimized
characteristics  are  expressed  as  functionals  on  the  set of
functions,  satisfying  the  solvability  conditions  of  inverse
boundary-value  problem.  Applications  are given for problems of
airfoil aerodynamic optimization.