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Published February 8, 1999 | public
Journal Article

Some examples of nonlinear homogenization involving nearly degenerate energies


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.

Additional Information

© 1999 The Royal Society. Received 9 September 1997; accepted 28 April 1998. This project took form when K.B. held a postdoctoral position and Sergei Kozlov visited the Courant Institute. Unfortunately, Sergei Kozlov did not live to see it completed. This work was partly supported by grants from the AFOSR (K.B.: F49620-95-1-0109), ARO (R.V.K.: DAAH04-95-1-0010) and the NSF (K.B.: CMS-9457573 and R.V.K.: DMS 94-04376 and DMS 94-02763).

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