46
Views
1
CrossRef citations to date
0
Altmetric
Articles

Homogenization of Monotone Problems with Uncertain Coefficients

&
Pages 432-441 | Received 25 Oct 2010, Accepted 27 Jun 2011, Published online: 24 Aug 2011

References

  • Allaire G. Homogenization and two-scale convergence . SIAM J. Math. Anal. , 23 6 : 1482 – 1518 , 1992 . doi: 10.1137/0523084 .
  • Bakhvalov N. and Panasenko G. Homogenization: Averaging Processes in Periodic Media . Mathematical Problems in the Mechanics of Composite Materials, Springer , 1989 .
  • Chiadò Piat V. and Defranceschi A. Homogenization of monotone operators . Nonlin. Anal. , 14 9 : 717 – 732 , 1990 . doi: 10.1016/0362-546X(90)90102-M .
  • Cioranescu , D. and Donato , P. 1999 . An Introduction to Homogenization , Oxford University Press .
  • Dal Maso G. Introduction to γ-convergence . Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser, Boston , 1993 .
  • Defranceschi , A. 1993 . An introduction to homogenization and G-convergence . Lecture notes, School on homogenization at the ICTP, Trieste September , 6–8 : 1 – 48 .
  • Franců , J. 1990 . Monotone operators. A survey directed to applications to differential equations . Appl Math. , 35 ( 6 ) : 257 – 301 .
  • Fusco , N. and Moscariello , G. 1987 . On the homogenization of quasilinear divergence structure operators . Ann. Mat. Pura Appl., IV. Ser. , 146 : 1 – 13 .
  • Hlaváček , I. , Chleboun , J. and Babuška , I. 2004 . Uncertain Input Data Problems and the Worst Scenario Method , North-Holland : Applied Mathematics and Mechanics .
  • Murat , F. and Tartar , L. 1997 . H-convergence , Birkhäuser : Topics in Mathematical Modelling of Composite Materials .
  • Nechvátal , L. 2006 . Worst scenario method in homogenization, linear case . Appl. Math. , 51 ( 3 ) : 263 – 294 .
  • Nechvátal , L. 2009 . Homogenization of monotone type problems with uncertain data . Tatra Mt. Math. Publ. , 43 : 163 – 171 .
  • Nguetseng G. A general convergence result for a functional related to the theory of homogenization . SIAM J. Math. Anal. , 20 3 : 608 – 623 , 1989 . doi: 10.1137/0520043 .
  • Nguetseng , G. and Svanstedt , N. 2011 . Σ-convergence . Banach J. Math. Anal. , 5 ( 1 ) : 101 – 135 .
  • Zeidler , E. 1990 . Nonlinear Functional Analysis and Its Applications IIB , New York : Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.