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On the Representation of Effective Energy Densities

Published online by Cambridge University Press:  15 August 2002

Christopher J. Larsen
Christopher J. Larsen*
Affiliation:
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, U.S.A.; cjlarsen@wpi.edu.
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Abstract

We consider the question raised in [1] of whether relaxed energydensities involving both bulk and surface energiescan be written as a sum of two functions, one depending on the net gradientof admissible functions, and the other on netsingular part.We show that, in general, they cannot. In particular, if the bulk densityis quasiconvex but not convex, thereexists a convex and homogeneous of degree 1 function of the jump such thatthere is no such representation.

Keywords

Relaxationquasiconvexityintegral representation.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 529 - 538
Copyright
© EDP Sciences, SMAI, 2000

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