Quasiconvexification in 3-D for a variational reformulation of an optimal design problem in conductivity

Nonlinear Analysis, Theory, Methods and Applications

Volumn 64, Issue 9, 2006, Pages 1962-1976

  Maestre, Faustino ^a   Pedregal, Pablo ^a  

^a UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

Author keywords

Dependence on the gradient of the state; Optimal design; Quasiconvexification; Relaxation; Young measure

Indexed keywords

CONSTRAINT THEORY; ELECTRIC FIELDS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES; VECTORS;

DEPENDENCE ON THE GRADIENT OF THE STATE; OPTIMAL DESIGN; QUASICONVEXIFICATION; YOUNG MEASURE;

OPTIMIZATION;

EID: 33344462804     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.07.032     Document Type: Article

References (17)

1. G. Allaire Shape Optimization by the Homogenization Method 2002 Springer Berlin
2. E. Aranda, P. Pedregal, Constrained envelope for a general class of design problems, Disc. Cont. Dyn. Syst., Supplement Volume, (2003) 30-41.
3. J.C. Bellido Explicit computation of the relaxed density coming from a three-dimensional optimal design problem Nonlinear Analysis 52 2003 1709 1726
4. M. Chipot Elements of Nonlinear Analysis 2000 Birkhäuser Basel
5. B. Dacorogna Direct Method in the Calculus of Variations 1989 Springer Berlin
6. I. Ekeland, and R. Téman Convex Analysis and Variational Problems 1999 SIAM Philadelphia
7. P.R. Kotiuga Clebsch potentials and the visualization of three-dimensional solenoidal vector fields IEEE Trans. Magn. 27 5 1991 3986 3989
8. R. Lipton, A.P. Velo, Optimal design of gradient field with applications to electrostatics, in: D. Cioranescu, J.L. Lions (Eds.), Nonlinear Partial Differential Equations and Their Applications, College de France Seminar, vol. XIV, 2002.
9. S.D. Nigam, R. Usha, and K. Swaminathan Divergence-free vectors fields J. Math. Phy. Sci. 14 5 1980 523 527
10. P. Pedregal Parametrized Measure and Variationals Principles 1997 Birkhauser Basel
11. P. Pedregal Constrained quasiconvexification of the square of the gradient of the state in optimal design Quart. Appl. Math. 62 3 2004 459 470
12. P. Pedregal Optimal design in 2-D conductivity for quadratic functionals in the field Proceedings of the Advanced NATO Conference in Non-linear homogenization Varsovia 2004
13. P. Pedregal, Vector variational problems and applications to optimal design, ESAIM-COCV 15 (2005) 357-381.
14. B.K. Shivamoggi Theoretical Fluid Dynamics 1998 Wiley New York
15. L. Tartar Remarks on optimal design problems G. Buttazzo G. Bouchitte P. Suquet Calculus of Variations, Homogenizacion and Continuum Mechasnics 1994 World Scientific Singapore 279 296
16. L. Tartar An introduction to the homogenization method in optimal design Lecture Notes in Mathematics vol. 1740 2000 Springer Berlin 47 156
17. C.S. Yih, Stream functions in three-dimensional flows, La Houille Blanche (3) (1957) 445-450.