Geodesic
An existence result for a nonconvex variational problem via regularity
Fonseca, Irene ; Fusco, Nicola1  ; Marcellini, Paolo 
1 Dipartimento di Matematica e Applicazioni Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy;
ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 69-95

Voir la notice de l'article provenant de la source Numdam

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 x-dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.

DOI : 10.1051/cocv:2002004
Classification : 49J45, 49K20, 35F30, 35R70
Keywords: nonconvex variational problems, uniform convexity, regularity, implicit differential equations

Fonseca, Irene  ; Fusco, Nicola 1 ; Marcellini, Paolo 

1 Dipartimento di Matematica e Applicazioni Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy; 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :