@article{article_761694, title={ON THE EXISTENCE OF SOLUTION FOR AN INVERSE PROBLEM}, journal={TWMS Journal of Applied and Engineering Mathematics}, volume={3}, pages={33–45}, year={2013}, author={Tajani, Chakir and Abouchabaka, Jaafar and Samouh, Nadia}, keywords={Inverse problem,Boundary detection problem,Shape optimization,Laplaceequation}, abstract={We consider a boundary detection problem. We present physical motivations. We formulate the problem as a shape optimization problem by introducing the Neumann condition of the accessible part in a cost functional to be minimized, which complicates the study of continuity state that requires more regularity of the free boundary. We show the existence of the optimal solution of the problem by the J. Haslinger and P. Neittaanm¨aki principle.}, number={1}, publisher={Işık University Press}