Geodesic
Higher Integrability for Solutions to Variational Problems with Fast Growth
Journal of convex analysis, Tome 18 (2011) no. 1, pp. 173-18.

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

We prove higher integrability properties of solutions to variational problems of minimizing $$ \int_\Omega [e^{f(\|\nabla u(x)\|)}+g(x,u(x))]\,dx $$ where $f$ is a convex function satisfying some additional conditions. 
@article{JCA_2011_18_1_JCA_2011_18_1_a8,
     author = {A. Cellina and M. Mazzola},
     title = {Higher {Integrability} for {Solutions} to {Variational} {Problems} with {Fast} {Growth}},
     journal = {Journal of convex analysis},
     pages = {173--18},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_1_JCA_2011_18_1_a8/}
}
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A. Cellina; M. Mazzola. Higher Integrability for Solutions to Variational Problems with Fast Growth. Journal of convex analysis, Tome 18 (2011) no. 1, pp. 173-18. http://geodesic.mathdoc.fr/item/JCA_2011_18_1_JCA_2011_18_1_a8/