Document Type

Article

Publication Date

11-1-2000

Publication Title

ESAIM-Control Optimisation and Calculus of Variations

Abstract

We consider the question raised in [1] of whether relaxed energy densities involving both bulk and surface energies can be written as a sum of two functions, one depending on the net gradient of admissible functions, and the other on net singular part. We show that, in general, they cannot. In particular, if the bulk density is quasiconvex but not convex, there exists a convex and homogeneous of degree 1 function of the jump such that there is no such representation.

Volume

5

First Page Number

529

Last Page Number

538

DOI

10.1051/cocv:2000120

Publisher Statement

© 2000, EDP Sciences. Available on publisher's site at http://dx.doi.org/10.1051/cocv:2000120.

Included in

Mathematics Commons

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