Some examples of nonlinear homogenization involving nearly degenerate energies

K. Bhattacharya, R. V. Kohn, S. Kozlov

Research output: Contribution to journalArticlepeer-review


We consider a specific class of nonlinear homogenization problems. The microstructure is a sort of checkerboard polycrystal, and the energy of the basic crystal is degenerate in one direction. We give matching upper and lower bounds for the homogenized energy. The motivation for this problem lies in the recent work of Bhattacharya & Kohn on shape-memory polycrystals. Our results show that a bound proved therein is nearly sharp.

Original languageEnglish (US)
Pages (from-to)567-583
Number of pages17
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1982
StatePublished - 1999


  • checkerboard microstructure
  • homogenization
  • optimal bounds
  • shape-memory polycrystals

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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