A shape optimization approach to free boundary value problems J. Haslinger Department of Metal Physics, Charles University Prague, Ke Karlovu 5, 121 16 Prague 2, Czech Republic T. Kozubek Department of Applied Mathematics, VSB-Technical University Ostrava, 17. listopadu 15, 708 33 Ostrava 8, Czech Republic K. Kunisch G.Peichl ∗ Department for Mathematics, University of Graz, Heinrichstrasse 36, A-8010 Graz, Austria Abstract This contribution combines a shape optimization approach to free boundary value problems of Bernoulli type with an embedding domain technique. A theoretical framework is developed which allows to prove continuous dependence of the primal and dual variables in the resulting saddle point problems with respect to the domain. This ensures the existence of a solution of a related shape optimization problem in a sufficiently large class of admissible domains. Key words: Shape optimization, embedding domain technique, Bernoulli problem ∗ Corresponding author Email addresses: haslin@apollo.karlov.mff.cuni.cz (J. Haslinger), tomas.kozubek@vsb.cz (T. Kozubek), karl.kunisch@uni-graz.at (K. Kunisch), gunther.peichl@uni-graz.at (G.Peichl). 1 Research was supported in part by the Fonds zur F¨orderung der Wissenschaft und Forschung under SFB03-18 ”Optimierung und Kontrolle”, by the AKTION ¨ Osterreich-Tschechische Republik under 32p9 and by the grant IAA1075005 of the Czech Academy of Sciences Preprint submitted to Journal of Mathematical Analysis and Applications22 August 2003