Young and H-measures for relaxation of multy-well energies
by
Neven Balenovic
MPI für Mathematik in den Naturwissenschaften, Leipzig, Germany and Department of Mathematics, University of Zagreb, Croatia
Coauthors: Nenad Antonic (MPI für Mathematik in den Naturwissenschaften, Leipzig, Germany and Department of Mathematics, University of Zagreb, Croatia), Marko Vrdoljak (MPI für Mathematik in den Naturwissenschaften, Leipzig, Germany and Department of Mathematics, University of Zagreb, Croatia)

Non-convex energy functionals are known to be lacking minimisers in the usual sense, due to the fact that minimising sequences tend to oscillate rapidly aiming to satisfy imposed restrictions, thus exhibiting microstructures. Mathematical tools known to be able to give some information on microstructures are Young measures (introduced in thirties by L. C. Young and applied in this context by L. Tartar in seventies) and H-measures (L. Tartar 1990 and independently P. Gerard 1991). Particularly, in the case of the multy-well energy minimisation, we use the above tools to construct generalised minimisers and obtain good bounds, following the ideas of Kohn, Ball & James and Tartar. The relevance of these results for real materials will be discussed as well.

Date received: March 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-24.