Geodesic
On the Bernoulli free boundary problem and related shape optimization problems
Mohammed Hayouni1 ; Antoine Henrot2 ; Nadia Samouh3
1Université Henri Poincaré, Vandoeuvre les Nancy, France
2Institut Élie Cartan Nancy, Vandoeuvre les Nancy, France
3Université Moulay Ismaïl, Meknès, Morocco
Interfaces and free boundaries, Tome 3 (2001) no. 1, pp. 1-13

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DOI

This paper deals with the classical Bernoulli free boundary problem. We are interested in solving some shape optimization problems related to this free boundary problem. We prove the continuous dependence of the solution with respect to the data K, working with Hausdorff convergence. We can deduce an existence result for a large class of shape optimization problems. Finally, we give some ideas for a numerical method, based on the use of conformal mappings, to solve such problems in two dimensions.
DOI : 10.4171/ifb/30
Classification : 46-XX, 60-XX
Mots-clés : Bernoulli free boundary, continuous dependence, shape optimization

Mohammed Hayouni  1   ; Antoine Henrot  2   ; Nadia Samouh  3

1 Université Henri Poincaré, Vandoeuvre les Nancy, France
2 Institut Élie Cartan Nancy, Vandoeuvre les Nancy, France
3 Université Moulay Ismaïl, Meknès, Morocco 
Mohammed Hayouni; Antoine Henrot; Nadia Samouh. On the Bernoulli free boundary problem and related shape optimization problems. Interfaces and free boundaries, Tome 3 (2001) no. 1, pp. 1-13. doi: 10.4171/ifb/30
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