On the integral representation of relaxed functionals with convex bounded constraints
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 16, Issue: 1, page 37-57
- ISSN: 1292-8119
Access Full Article
top
Abstract
topHow to cite
topAnza Hafsa, Omar. "On the integral representation of relaxed functionals with convex bounded constraints." ESAIM: Control, Optimisation and Calculus of Variations 16.1 (2010): 37-57. <http://eudml.org/doc/250725>.
@article{AnzaHafsa2010,
abstract = {
We study the integral representation of relaxed functionals in the multi-dimensional calculus of variations, for integrands which are finite in a convex bounded set with nonempty interior and infinite elsewhere.
},
author = {Anza Hafsa, Omar},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Relaxation; convex constraints; integral representation; relaxation},
language = {eng},
month = {1},
number = {1},
pages = {37-57},
publisher = {EDP Sciences},
title = {On the integral representation of relaxed functionals with convex bounded constraints},
url = {http://eudml.org/doc/250725},
volume = {16},
year = {2010},
}
TY - JOUR
AU - Anza Hafsa, Omar
TI - On the integral representation of relaxed functionals with convex bounded constraints
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/1//
PB - EDP Sciences
VL - 16
IS - 1
SP - 37
EP - 57
AB -
We study the integral representation of relaxed functionals in the multi-dimensional calculus of variations, for integrands which are finite in a convex bounded set with nonempty interior and infinite elsewhere.
LA - eng
KW - Relaxation; convex constraints; integral representation; relaxation
UR - http://eudml.org/doc/250725
ER -
References
top- E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal.86 (1984) 125–145.
- O. Anza Hafsa and J.-P. Mandallena, Relaxation of variational problems in two-dimensional nonlinear elasticity. Ann. Mat. Pura Appl.186 (2007) 187–198.
- O. Anza Hafsa and J.-P. Mandallena, Relaxation theorems in nonlinear elasticity. Ann. Inst. H. Poincaré, Anal. Non Linéaire25 (2008) 135–148.
- J.M. Ball and F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals. J. Funct. Anal.58 (1984) 225–253.
- H. Ben Belgacem, Relaxation of singular functionals defined on Sobolev spaces. ESAIM: COCV5 (2000) 71–85.
- L. Carbone and R. De Arcangelis, Unbounded functionals in the calculus of variations, Representation, relaxation, and homogenization, Monographs and Surveys in Pure and Applied Mathematics125. Chapman & Hall/CRC, Boca Raton, FL, USA (2002).
- B. Dacorogna, Direct methods in the Calculus of Variations. Springer-Verlag (1989).
- B. Dacorogna and P. Marcellini, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases. Acta Math.178 (1997) 1–37.
- B. Dacorogna and P. Marcellini, Implicit partial differential equations, Progress in Nonlinear Differential Equations and their Applications37. Birkhäuser Boston, Inc., Boston, MA, USA (1999).
- I. Fonseca, The lower quasiconvex envelope of the stored energy function for an elastic crystal. J. Math. Pures Appl.67 (1988) 175–195.
- D. Kinderlehrer and P. Pedregal, Characterizations of Young measures generated by gradients. Arch. Rational Mech. Anal.115 (1991) 329–365.
- C.B. Morrey, Quasiconvexity and lower semicontinuity of multiple integrals. Pacific J. Math.2 (1952) 25–53.
- S. Müller, A sharp version of Zhang's theorem on truncating sequences of gradients. Trans. Amer. Math. Soc.351 (1999) 4585–4597.
- T.R. Rockafellar and J.-B. Wets, Variational analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 317. Springer-Verlag, Berlin (1998).
- M. Wagner, On the lower semicontinuous quasiconvex envelope for unbounded integrands. To appear on ESAIM: COCV (to appear).
- M. Wagner, Quasiconvex relaxation of multidimensional control problems. Adv. Math. Sci. Appl. (to appear).
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.