Geodesic
Some remarks on variational problems for functionals with $L\ln L$ growth
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 164-178 
G. A. Seregin. Some remarks on variational problems for functionals with $L\ln L$ growth. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 164-178. http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a9/
@article{ZNSL_1994_213_a9,
     author = {G. A. Seregin},
     title = {Some remarks on variational problems for functionals with $L\ln L$ growth},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {164--178},
     year = {1994},
     volume = {213},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a9/}
}
TY  - JOUR
AU  - G. A. Seregin
TI  - Some remarks on variational problems for functionals with $L\ln L$ growth
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1994
SP  - 164
EP  - 178
VL  - 213
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a9/
LA  - en
ID  - ZNSL_1994_213_a9
ER  - 
%0 Journal Article
%A G. A. Seregin
%T Some remarks on variational problems for functionals with $L\ln L$ growth
%J Zapiski Nauchnykh Seminarov POMI
%D 1994
%P 164-178
%V 213
%U http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a9/
%G en
%F ZNSL_1994_213_a9

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Regularity for minimizers of the functional $\int_\Omega|\nabla v|\ln(1+|\nabla v|)\,dx$ on a set of vector-valued functions $v\colon\Omega\subset\mathbb R^n\to\mathbb R^n$, taking prescribed values on the boundary $\partial\Omega$, is studied. It is shown that solution of the dual variational problem belong to the class $W^1_{2,\mathrm{loc}}$. In the case $n=2$ a higher integrability for minimizers of the direct variational problem is proved. Bibliography: 5 titles.