On the representation of effective energy densities

Christopher J. Larsen

ESAIM: Control, Optimisation and Calculus of Variations (2000)

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

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Larsen, Christopher J.. "On the representation of effective energy densities." ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 529-538. <http://eudml.org/doc/90581>.

@article{Larsen2000,
author = {Larsen, Christopher J.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {relaxation; quasiconvexity; integral representation; bulk and surface integrals},
language = {eng},
pages = {529-538},
publisher = {EDP Sciences},
title = {On the representation of effective energy densities},
url = {http://eudml.org/doc/90581},
volume = {5},
year = {2000},
}

TY - JOUR
AU - Larsen, Christopher J.
TI - On the representation of effective energy densities
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2000
PB - EDP Sciences
VL - 5
SP - 529
EP - 538
LA - eng
KW - relaxation; quasiconvexity; integral representation; bulk and surface integrals
UR - http://eudml.org/doc/90581
ER -

References

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  1. [1] R. Choksi and I. Fonseca, Bulk and interfacial energy densities for structured deformations of continua, Arch. Rational Mech. Anal. 138 ( 1997) 37-103. Zbl0891.73078MR1463803
  2. [2] B. Dacorogna, Direct Methods in the Calculus of Variations. Springer-Verlag, Berlin ( 1989). Zbl0703.49001MR990890
  3. [3] E. De Giorgi and L. Ambrosio, Un nuovo tipo di funzionale del calcolo delle variazioni. Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Suppl. 82 ( 1988) 199-210. Zbl0715.49014MR1152641
  4. [4] G. Del Piero and D.R. Owen, Structured deformations of continua. Arch. Rational Mech. Anal. 124 ( 1993) 99-155. Zbl0795.73005MR1237908
  5. [5] L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton ( 1992). Zbl0804.28001MR1158660
  6. [6] I. Fonseca, S. Müller and P. Pedregal, Analysis of concentration and oscillation effects generated by gradients. SIAM J. Math. Anal. 29 ( 1998) 736-756. Zbl0920.49009MR1617712
  7. [7] J. Kristensen, Lower semicontinuity in spaces of weakly differentiable functions. Math. Ann. 313 ( 1999) 653-710. Zbl0924.49012MR1686943
  8. [8] C.J. Larsen, Quasiconvexincation in W1,1 and optimal jump microstructure in BV relaxation. SIAM J. Math. Anal. 29 ( 1998) 823-848. Zbl0915.49005MR1617734
  9. [9] S. Müller, On quasiconvex functions which are homogeneous of degree 1. Indiana Univ. Math. J. 41 ( 1992) 295-301. Zbl0736.26006MR1160915

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