Free Access
Volume 22, Number 2, April-June 2016
Page(s) 309 - 337
Published online 23 February 2016
  1. L. Ambrosio and G. Buttazzo, An optimal design problem with perimeter penalization. Calc. Var. Partial Differ. Equ. 1 (1993) 55–69. [CrossRef] [MathSciNet] [Google Scholar]
  2. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Clarendon Oxford, Press (2000). [Google Scholar]
  3. J. Bello, E. Fernández-Cara, J. Lemoine and J. Simon, The differentiability of the drag with respect to the variations of a Lipschitz domain in a Navier–Stokes flow. SIAM J. Control Optim. 35 (1997) 626–640. [CrossRef] [MathSciNet] [Google Scholar]
  4. J. F. Blowey and C. M. Elliott, The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysis. Eur. J. Appl. Math. 2 (1991) 233–280. [CrossRef] [MathSciNet] [Google Scholar]
  5. T. Borrvall and J. Petersson, Topology optimization of fluids in Stokes flow. Internat. J. Numer. Methods Fluids 41 (2003) 77–107. [CrossRef] [MathSciNet] [Google Scholar]
  6. B. Bourdin and A. Chambolle, Design-dependent loads in topology optimization. ESAIM: COCV 9 (2003) 19–48. [CrossRef] [EDP Sciences] [Google Scholar]
  7. D. Bucur and G. Buttazzo, Variational Methods in Shape Optimization Problems. Progr. Nonlin. Differ. Equ. Appl. Springer (2006). [Google Scholar]
  8. G. Buttazzo and G. Dal Maso, Shape optimization for Dirichlet problems: Relaxed formulation and optimality conditions. Appl. Math. Optim. 23 (1991) 17–49. [Google Scholar]
  9. G. Dal Maso, An Introduction to Γ-convergence. Progr. Nonlin. Differ. Equ. Appl. Birkhäuser (1993). [Google Scholar]
  10. G. Dal Masos and U. Mosco, Wiener’s criterion and Γ-convergence. Appl. Math. Optim. 15 (1987) 15–63. [CrossRef] [MathSciNet] [Google Scholar]
  11. M.C. Delfour and J.P. Zolésio, Shapes and Geometries: Analysis, Differential Calculus and Optimization. Adv. Des. Control. SIAM (2001). [Google Scholar]
  12. M.C. Delfour and J.P. Zolésio, Shape Derivatives for Nonsmooth Domains. Optimal Control of Partial Differential Equations, edited by K.-H. Hoffmann and W. Krabs. In vol. 149 of Lect. Notes Control and Inform. Sci. Springer (1991) 38–55. [Google Scholar]
  13. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Mathematical Chemistry Series. CRC PressINC (1992). [Google Scholar]
  14. G.P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Springer (2011). [Google Scholar]
  15. H. Garcke and C. Hecht, A phase field approach for shape and topology optimization in Stokes flow. New Trends in Shape Optimization. Edited by Pratelli, Aldo, Leugering, Günter. ISNM Series, vol. 166. Birkhäuser, Basel (2014). [Google Scholar]
  16. H. Garcke and C. Hecht, Shape and topology optimization in Stokes flow with a phase field approach. Appl. Math. Optim. 73 (2016) 23–70. [CrossRef] [MathSciNet] [Google Scholar]
  17. H. Garcke, C. Hecht, M. Hinze and C. Kahle, Numerical approximation of phase field based shape and topology optimization for fluids. Preprint arXiv:1405.3480 (2014). [Google Scholar]
  18. C. Hecht, Shape and topology optimization in fluids using a phase field approach and an application in structural optimization. Dissertation, University of Regensburg (2014). [Google Scholar]
  19. B. Kawohl, A. Cellina and A. Ornelas, Optimal Shape Design: Lectures Given at the Joint C.I.M./C.I.M.E. Summer School Held in Troia (Portugal), June 1-6 (1998). In Lect. Notes Math./C.I.M.E. Foundation Subseries. Springer (2000). [Google Scholar]
  20. L. Modica, The gradient theory of phase transitions and the minimal interface criterion. Arch. Ration. Mech. Anal. 98 (1987) 123–142. [Google Scholar]
  21. S. Schmidt and V. Schulz, Shape Derivatives for General Objective Functions and the Incompressible Navier–Stokes Equations. Control Cybernet. 39 (2010) 677–713. [MathSciNet] [Google Scholar]
  22. R.E. Showalter, Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations. In vol. 49 of Math. Surv. Monographs. American Mathematical Society (1997). [Google Scholar]
  23. J. Simon, Domain variation for drag in Stokes flow. Control Theory of Distributed Parameter Systems and Applications, edited by X. Li and J. Yong. In vol. 159 of Lect. Notes Control and Inform. Sci. Springer (1991) 28–42. [Google Scholar]
  24. H. Sohr, The Navier-Stokes Equations: An Elementary Functional Analytic Approach. Birkhäuser (2001). [Google Scholar]
  25. J. Sokolowski and J.P. Zolésio, Introduction to Shape Optimization: Shape Sensitivity Analysis. Springer (1992). [Google Scholar]
  26. P. Sternberg, The effect of a singular perturbation on nonconvex variational problems. Arch. Ration. Mech. Anal. 101 (1988) 209–260. [Google Scholar]
  27. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis. Stud. Math. Appl. North-Holland (1977). [Google Scholar]
  28. F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen. Vieweg (2009). [Google Scholar]
  29. E. Zeidler, Nonlinear Functional Analysis and Its Applications: Part 2B: Nonlinear Monotone Operators. Springer (1990). [Google Scholar]
  30. E. Zeidler, Nonlinear Functional Analysis and Its Applications: Part IV: Applications to Mathematical Physics. Springer (1997). [Google Scholar]

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