Geodesic
Some Remarks on Quasiconvexity, Inner Variations, and Optimal Meshes
Journal of convex analysis, Tome 15 (2008) no. 2, pp. 381-393

Voir la notice de l'article provenant de la source Heldermann Verlag

We explore a formulation of quasiconvexity in terms of inner variations instead of variations of the dependent variable. This leads to a specific transformation of integrands that is stable for rank-one convexity, quasiconvexity, and polyconvexity, but not for convexity. An interesting application of these ideas is concerned with the analysis of optimal adaptive meshes for variational problems. This theme is not new either in the analytical or numerical treatment. We complete the discussion with some easy examples in dimension one, and defer the much more complex situation in higher dimension for a later work. An interesting point is that our remarks are valid when the number of components for fields is not greater than the number of independent variables.
Classification : 37C40, 37E05, 49J45
Mots-clés : Weak convergence, Young measure, invariant measure 
@article{JCA_2008_15_2_JCA_2008_15_2_a13,
     author = {P. Pedregal},
     title = {Some {Remarks} on {Quasiconvexity,} {Inner} {Variations,} and {Optimal} {Meshes}},
     journal = {Journal of convex analysis},
     pages = {381--393},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a13/}
}
TY  - JOUR
AU  - P. Pedregal
TI  - Some Remarks on Quasiconvexity, Inner Variations, and Optimal Meshes
JO  - Journal of convex analysis
PY  - 2008
SP  - 381
EP  - 393
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a13/
ID  - JCA_2008_15_2_JCA_2008_15_2_a13
ER  - 
%0 Journal Article
%A P. Pedregal
%T Some Remarks on Quasiconvexity, Inner Variations, and Optimal Meshes
%J Journal of convex analysis
%D 2008
%P 381-393
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a13/
%F JCA_2008_15_2_JCA_2008_15_2_a13
P. Pedregal. Some Remarks on Quasiconvexity, Inner Variations, and Optimal Meshes. Journal of convex analysis, Tome 15 (2008) no. 2, pp. 381-393. http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a13/