# On the Representation of Effective Energy Densities

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 5, page 529-538
- ISSN: 1292-8119

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topLarsen, Christopher J.. "On the Representation of Effective Energy Densities." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 529-538. <http://eudml.org/doc/197301>.

@article{Larsen2010,

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.
},

author = {Larsen, Christopher J.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Relaxation; quasiconvexity; integral representation.; relaxation; integral representation; bulk and surface integrals},

language = {eng},

month = {3},

pages = {529-538},

publisher = {EDP Sciences},

title = {On the Representation of Effective Energy Densities},

url = {http://eudml.org/doc/197301},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Larsen, Christopher J.

TI - On the Representation of Effective Energy Densities

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 5

SP - 529

EP - 538

AB -
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.

LA - eng

KW - Relaxation; quasiconvexity; integral representation.; relaxation; integral representation; bulk and surface integrals

UR - http://eudml.org/doc/197301

ER -

## References

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- S. Müller, On quasiconvex functions which are homogeneous of degree 1. Indiana Univ. Math. J.41 (1992) 295-301.

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