## On a Bernoulli problem with geometric constraints

*Laurain , Antoine*;

*Privat , Yannick*;

- Publisher: EDP Sciences
Related identifiers: doi: 10.1051/cocv/2010049 - Subject: parameterization method | shape optimization | [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP] | free boundary problem | Bernoulli condition | 49J10, 35J25, 35N05, 65P05

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[3] A. Beurling. On free boundary problems for the Laplace equation, volume 1 of Seminars on analytic functions. Institute Advance Studies Seminars Princeton, 1957.

[4] F. Bouchon, S. Clain, and R. Touzani. Numerical solution of the free boundary Bernoulli problem using a level set formulation. Comput. Methods Appl. Mech. Engrg., 194(36-38):3934-3948, 2005.

[5] E. N. Dancer and D. Daners. Domain perturbation for elliptic equations subject to Robin boundary conditions. J. Differential Equations, 138(1):86-132, 1997.

[6] M. C. Delfour and J.-P. Zole´sio. Shapes and geometries, volume 4 of Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2001. Analysis, differential calculus, and optimization.

[7] L. C. Evans. Partial differential equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1998.

[8] A. Fasano. Some free boundary problems with industrial applications. In Shape optimization and free boundaries (Montreal, PQ, 1990), volume 380 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pages 113-142. Kluwer Acad. Publ., Dordrecht, 1992.

[9] M. Flucher and M. Rumpf. Bernoulli's free boundary problem, qualitative theory and numerical approximation. Journal fu¨r die reine und angewandte Mathematik, 486:165-204, 1997.

[10] A. Friedman. Free boundary problem in fluid dynamics. Aste´risque, (118):55-67, 1984. Variational methods for equilibrium problems of fluids (Trento, 1983).

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