Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The -dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.
Mots-clés : nonconvex variational problems, uniform convexity, regularity, implicit differential equations
@article{COCV_2002__7__69_0,
author = {Fonseca, Irene and Fusco, Nicola and Marcellini, Paolo},
title = {An existence result for a nonconvex variational problem via regularity},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {69--95},
publisher = {EDP-Sciences},
volume = {7},
year = {2002},
doi = {10.1051/cocv:2002004},
mrnumber = {1925022},
zbl = {1044.49011},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2002004/}
}
TY - JOUR AU - Fonseca, Irene AU - Fusco, Nicola AU - Marcellini, Paolo TI - An existence result for a nonconvex variational problem via regularity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 69 EP - 95 VL - 7 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2002004/ DO - 10.1051/cocv:2002004 LA - en ID - COCV_2002__7__69_0 ER -
%0 Journal Article %A Fonseca, Irene %A Fusco, Nicola %A Marcellini, Paolo %T An existence result for a nonconvex variational problem via regularity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 69-95 %V 7 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2002004/ %R 10.1051/cocv:2002004 %G en %F COCV_2002__7__69_0
Fonseca, Irene; Fusco, Nicola; Marcellini, Paolo. An existence result for a nonconvex variational problem via regularity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 69-95. doi : 10.1051/cocv:2002004. http://archive.numdam.org/articles/10.1051/cocv:2002004/
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