Free Access
Issue
ESAIM: COCV
Volume 18, Number 1, January-March 2012
Page(s) 157 - 180
DOI https://doi.org/10.1051/cocv/2010049
Published online 02 December 2010
  1. A. Acker, An extremal problem involving current flow through distributed resistance. SIAM J. Math. Anal. 12 (1981) 169–172. [CrossRef] [MathSciNet] [Google Scholar]
  2. C. Atkinson and C.R. Champion, Some boundary-value problems for the equation ∇·(|∇ϕ| Nϕ) = 0. Quart. J. Mech. Appl. Math. 37 (1984) 401–419. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Beurling, On free boundary problems for the Laplace equation, Seminars on analytic functions 1. Institute for Advanced Studies, Princeton (1957). [Google Scholar]
  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. Eng. 194 (2005) 3934–3948. [CrossRef] [Google Scholar]
  5. E.N. Dancer and D. Daners, Domain perturbation for elliptic equations subject to Robin boundary conditions. J. Differ. Equ. 138 (1997) 86–132. [CrossRef] [Google Scholar]
  6. M.C. Delfour and J.-P. Zolésio, Shapes and geometries – Analysis, differential calculus, and optimization, Advances in Design and Control 4. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2001). [Google Scholar]
  7. L.C. Evans, Partial differential equations, Graduate Studies in Mathematics 19. American Mathematical Society, Providence (1998). [Google Scholar]
  8. A. Fasano, Some free boundary problems with industrial applications, in Shape optimization and free boundaries (Montreal, PQ, 1990), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 380, Kluwer Acad. Publ., Dordrecht (1992) 113–142. [Google Scholar]
  9. M. Flucher and M. Rumpf, Bernoulli’s free boundary problem, qualitative theory and numerical approximation. J. Reine Angew. Math. 486 (1997) 165–204. [MathSciNet] [Google Scholar]
  10. A. Friedman, Free boundary problem in fluid dynamics, in Variational methods for equilibrium problems of fluids, Trento 1983, Astérisque 118 (1984) 55–67. [Google Scholar]
  11. A. Friedman, Free boundary problems in science and technology. Notices Amer. Math. Soc. 47 (2000) 854–861. [MathSciNet] [Google Scholar]
  12. P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics 24. Pitman (Advanced Publishing Program), Boston (1985). [Google Scholar]
  13. J. Haslinger, T. Kozubek, K. Kunisch and G. Peichl, Shape optimization and fictitious domain approach for solving free boundary problems of Bernoulli type. Comp. Optim. Appl. 26 (2003) 231–251. [CrossRef] [Google Scholar]
  14. J. Haslinger, K. Ito, T. Kozubek, K. Kunisch and G. Peichl, On the shape derivative for problems of Bernoulli type. Interfaces in Free Boundaries 11 (2009) 317–330. [CrossRef] [Google Scholar]
  15. A. Henrot and M. Pierre, Variation et optimisation de formes – Une analyse géométrique, Mathématiques & Applications 48. Springer, Berlin (2005). [Google Scholar]
  16. A. Henrot and H. Shahgholian, Existence of classical solutions to a free boundary problem for the p-Laplace operator. I. The exterior convex case. J. Reine Angew. Math. 521 (2000) 85–97. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Henrot and H. Shahgholian, Existence of classical solutions to a free boundary problem for the p-Laplace operator. II. The interior convex case. Indiana Univ. Math. J. 49 (2000) 311–323. [MathSciNet] [Google Scholar]
  18. A. Henrot and H. Shahgholian, The one phase free boundary problem for the p-Laplacian with non-constant Bernoulli boundary condition. Trans. Amer. Math. Soc. 354 (2002) 2399–2416. [CrossRef] [MathSciNet] [Google Scholar]
  19. K. Ito, K. Kunisch and G.H. Peichl, Variational approach to shape derivatives for a class of Bernoulli problems. J. Math. Anal. Appl. 314 (2006) 126–149. [CrossRef] [Google Scholar]
  20. C.T. Kelley, Iterative methods for optimization, Frontiers in Applied Mathematics 18. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1999). [Google Scholar]
  21. V.A. Kondratév, Boundary value problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Obšč. 16 (1967) 209–292. [MathSciNet] [Google Scholar]
  22. C.M. Kuster, P.A. Gremaud and R. Touzani, Fast numerical methods for Bernoulli free boundary problems. SIAM J. Sci. Comput. 29 (2007) 622–634. [CrossRef] [MathSciNet] [Google Scholar]
  23. J. Lamboley and A. Novruzi, Polygons as optimal shapes with convexity constraint. SIAM J. Control Optim. 48 (2009) 3003–3025. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Lindgren and Y. Privat, A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition. Nonlinear Anal. 67 (2007) 2497–2505. [CrossRef] [MathSciNet] [Google Scholar]
  25. J. Nocedal and S.J. Wright, Numerical optimization. Springer Series in Operations Research and Financial Engineering, Springer, New York, 2nd edition (2006). [Google Scholar]
  26. J.R. Philip, n-diffusion. Austral. J. Phys. 14 (1961) 1–13. [CrossRef] [MathSciNet] [Google Scholar]
  27. J. Sokołowski and J.-P. Zolésio, Introduction to shape optimization : Shape sensitivity analysis, Springer Series in Computational Mathematics 16. Springer-Verlag, Berlin (1992). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.