References
- Braides , A and Defranceschi , A . 1998 . Homogenization of Multiple Integrals , Oxford : Oxford University Press .
- Jikov , VV , Kozlov , SM and Oleinik , OA . 1994 . Homogenization of Differential Operators and Integral Functionals , Berlin : Springer-Verlag .
- Bensoussan , A , Lions , JL and Papanicolaou , GC . 1978 . Asymptotic Analysis for Periodic Structures , North Holland : Amsterdam .
- Allaire , G and Briane , M . 1996 . Multiscale convergence and reiterated homogenization . P. Roy. Soc. Edinb. , 126A : 297 – 342 .
- Braides , A and Lukkassen , D . 2000 . Reiterated homogenization of integral functionals . Math. Mod. Meth. Appl. Sci. , 10 : 47 – 71 .
- Lukkassen , D . 1996 . “ Formulae and bounds connected to optimal design and homogenization of partial differential operators and integral functionals ” . In Ph.D. thesis, Depatment of Mathematics , Norway : Tromsö University .
- Lions , J-L . 2000 . Reiterated homogenization of monotone operators . C. R. Acad. Sci. Paris, Ser. I, Math. , 330 : 675 – 680 .
- Lions , J-L . 2001 . Reiterated homogenization of nonlinear monotone operators . Chin. Ann. Math., Ser. B , 22 : 1 – 14 .
- Lukkassen , D . 2001 . Reiterated homogenization of non-standard Lagrangians . C. R. Acad. Sci., Paris, Ser. I, Math , 332 : 999 – 1004 .
- Lukkassen , D and Milton , GW . 2002 . “ On hierarchical structures and reiterated homogenization ” . In Proceedings of the Conference on Function Spaces, Interpolation Theory and Related Topics in Honour of Jaak Peetre on his 65th Birthday , 311 – 324 . Berlin : Walter de Gruyter . August 17–22, 2000
- Lukkassen , D , Nguetseng , G and Wall , P . 2002 . Two scale convergence . Int. J. Pure Appl. Math. , 2 : 35 – 86 .
- Lukkassen , D , Meidell , A and Wall , P . 2008 . Multiscale homogenization of monotone operators . Discrete Cont. Dyn.-A. , 22 : 711 – 727 .
- Lurie , KA and Cherkaev , AV . 1997 . “ Effective characteriztics of composite materials and the optimal design of structural elements ” . In Topics in the Mathematical Modelling of Composite Materials, 175-258, Progress in Nonlinear Differential Equations and their Applications , Vol. 31 , Boston, MA : Birkhäuser Boston .
- Lukkassen , D . 1996 . Some sharp estimates connected to the homogenized p-Laplacian equation . ZAMM-Z.Angew. Math. Mech. , 76 : 603 – 604 .
- Lukkassen , D , Meidell , A and Wall , P . 2007 . Bounds on the effective behaviour of a homogenized Reynold-type equation . J. Funct. Spaces Appl. , 5 : 133 – 150 .
- Keller , JB . 1964 . A theorem on the conductivity of a composite medium . J. Math. Phys , 5 ( 4 ) : 548 – 549 .
- Dychne , AM . 1970 . Conductivity of a two-phase two-dimensional system . J. Exper. Theor. Phys , 59 ( 7 ) : 110 – 115 .