Free Access
Issue
ESAIM: M2AN
Volume 43, Number 1, January-February 2009
Page(s) 3 - 32
DOI https://doi.org/10.1051/m2an/2008038
Published online 16 October 2008
  1. G. Allaire, Shape optimization by the homogenization method, Applied Mathematical Sciences 146. Springer-Verlag, New York (2002). [Google Scholar]
  2. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems & Control: Foundations & Applications. Birkhäuser Boston Inc., Boston, USA (1997). With appendices by M. Falcone and P. Soravia. [Google Scholar]
  3. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques & Applications 17 (Berlin) [Mathematics & Applications]. Springer-Verlag, Paris (1994). [Google Scholar]
  4. M.P. Bendsøe and O. Sigmund, Topology optimization, Theory, methods and applications. Springer-Verlag, Berlin (2003). [Google Scholar]
  5. L. Borcea, Electrical impedance tomography. Inverse Problems 18 (2002) R99–R136. [CrossRef] [Google Scholar]
  6. S.C. Brenner and L. Ridgway Scott, The mathematical theory of finite element methods, Texts in Applied Mathematics 15. Springer-Verlag, New York (1994). [Google Scholar]
  7. P. Cannarsa and H. Frankowska, Some characterizations of optimal trajectories in control theory. SIAM J. Control Optim. 29 (1991) 1322–1347. [CrossRef] [MathSciNet] [Google Scholar]
  8. P. Cannarsa and H. Frankowska, Value function and optimality conditions for semilinear control problems. Appl. Math. Optim. 26 (1992) 139–169. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Cannarsa and H. Frankowska, Value function and optimality condition for semilinear co problems. II. Parabolic case. Appl. Math. Optim. 33 (1996) 1–33. [CrossRef] [MathSciNet] [Google Scholar]
  10. P. Cannarsa and C. Sinestrari, Semiconcave functions, Hamilton-Jacobi equations, and optimal control, Progress in Nonlinear Differential Equations and their Applications 58. Birkhäuser Boston Inc., Boston, USA (2004). [Google Scholar]
  11. J. Carlsson, Symplectic reconstruction of data for heat and wave equations. Preprint (2008) http://arxiv.org/abs/0809.3621. [Google Scholar]
  12. J. Céa, S. Garreau, P. Guillaume and M. Masmoudi, The shape and topological optimizations connection. Comput. Methods Appl. Mech. Engrg. 188 (2000) 713–726. IV WCCM, Part II (Buenos Aires, 1998). [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Cheney and D. Isaacson, Distinguishability in impedance imaging. IEEE Trans. Biomed. Eng. 39 (1992) 852–860. [CrossRef] [PubMed] [Google Scholar]
  14. F.H. Clarke, Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series in Mathematics. John Wiley and Sons, Inc. (1983). [Google Scholar]
  15. M.G. Crandall, L.C. Evans and P.-L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 282 (1984) 487–502. [CrossRef] [MathSciNet] [Google Scholar]
  16. M.G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 (1992) 1–67. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Crouzeix and V. Thomée, The stability in Lp and Formula of the L2-projection onto finite element function spaces. Math. Comp. 48(178) (1987) 521–532. [Google Scholar]
  18. B. Dacorogna, Direct methods in the calculus of variations, Appl. Math. Sci. 78. Springer-Verlag, Berlin (1989). [Google Scholar]
  19. H.W. Engl, M. Hanke and A. Neubauer, Regularization of inverse problems, Mathematics and its Applications 375. Kluwer Academic Publishers Group, Dordrecht (1996). [Google Scholar]
  20. L.C. Evans, Partial differential equations, Graduate Studies in Mathematics 19. American Mathematical Society, Providence, USA (1998). [Google Scholar]
  21. H. Frankowska, Contingent cones to reachable sets of control systems. SIAM J. Control Optim. 27 (1989) 170–198. [CrossRef] [MathSciNet] [Google Scholar]
  22. J. Goodman, R.V. Kohn and L. Reyna, Numerical study of a relaxed variational problem from optimal design. Comput. Methods Appl. Mech. Engrg. 57 (1986) 107–127. [CrossRef] [MathSciNet] [Google Scholar]
  23. E. Hairer, C. Lubich and G. Wanner, Geometric numerical integration, Structure-preserving algorithms for ordinary differential equations, Springer Series in Computational Mathematics 31. Springer-Verlag, Berlin (2002). [Google Scholar]
  24. B. Kawohl, J. Stará and G. Wittum, Analysis and numerical studies of a problem of shape design. Arch. Rational Mech. Anal. 114 (1991) 349–363. [CrossRef] [MathSciNet] [Google Scholar]
  25. R.V. Kohn and A. McKenney, Numerical implementation of a variational method for electrical impedance tomography. Inverse Problems 6 (1990) 389–414. [CrossRef] [MathSciNet] [Google Scholar]
  26. R.V. Kohn and G. Strang, Optimal design and relaxation of variational problems. I. Comm. Pure Appl. Math. 39 (1986) 113–137. [CrossRef] [MathSciNet] [Google Scholar]
  27. R.V. Kohn and G. Strang, Optimal design and relaxation of variational problems. II. Comm. Pure Appl. Math. 39 (1986) 139–182. [CrossRef] [MathSciNet] [Google Scholar]
  28. R.V. Kohn and G. Strang, Optimal design and relaxation of variational problems. III. Comm. Pure Appl. Math. 39 (1986) 353–377. [CrossRef] [MathSciNet] [Google Scholar]
  29. F. Natterer, The mathematics of computerized tomography, Classics in Applied Mathematics 32. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA (2001). Reprint of the 1986 original. [Google Scholar]
  30. O. Pironneau, Optimal shape design for elliptic systems, Springer Series in Computational Physics. Springer-Verlag, New York (1984). [Google Scholar]
  31. R.T. Rockafellar, Convex analysis, Princeton Mathematical Series 28. Princeton University Press, Princeton, USA (1970). [Google Scholar]
  32. M. Sandberg, Convergence rates for numerical approximations of an optimally controlled Ginzburg-Landau equation. Preprint (2008) http://arxiv.org/abs/0809.1834. [Google Scholar]
  33. M. Sandberg and A. Szepessy, Convergence rates of symplectic Pontryagin approximations in optimal control theory. ESAIM: M2AN 40 (2006) 149–173. [CrossRef] [EDP Sciences] [Google Scholar]
  34. D. Tataru, Viscosity solutions for Hamilton-Jacobi equations with unbounded nonlinear term: a simplified approach. J. Diff. Eq. 111 (1994) 123–146. [CrossRef] [Google Scholar]
  35. A.N. Tikhonov and V.Y. Arsenin, Solutions of ill-posed problems, in Scripta Series in Mathematics, V.H. Winston & Sons, Washington, D.C., John Wiley & Sons, New York (1977). Translated from the Russian, Preface by translation editor F. John. [Google Scholar]
  36. C.R. Vogel, Computational methods for inverse problems, Frontiers in Applied Mathematics 23. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2002). With a foreword by H.T. Banks. [Google Scholar]
  37. A. Wexler, B. Fry and M.R. Neuman, Impedance-computed tomography algorithm and system. Appl. Opt. 24 (1985) 3985–3992. [CrossRef] [PubMed] [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.

Recommended for you