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Lower and upper bounds for multiwell variational problems and optimal structures of multiphase composites.
by
Andrej Cherkaev
University of Utah
A new lower bound for multiwell variational problems (Localized Polyconvex Envelope) is suggested. It uses a combination of inequalities for a range of oscillating minimizer's gradient and polyconvexity. The inequalities are established using the rank-one connection of the ranges of gradients in different wells. The procedure is applied to the problem of structure of multiphase composites of minimal conductivity. Optimal structures and the lower bound for effective conductivity are found.
Date received: February 26, 2008
Copyright © 2008 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 # caws-57.