Geodesic
Variational problem with an obstacle in $\mathbb R^N$ for a~class of quadratic functionals
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 39, Tome 362 (2008), pp. 15-47

Voir la notice de l'article provenant de la source Math-Net.Ru

A variational problem with an obstacle for a certain class of quadratic functionals is considered. It is assumed that admissible vector-valued functions satisfy the Dirichlet boundary condition and the obstacle is a given smooth $(N-1)$-dimensional surface $S$ in $\mathbb R^N$. It is not supposed that the surface $S$ is bounded. It is proved that any minimizer $u$ of such an obstacle problem is a partially smooth function up to the boundary of prescribed domain. It is shown that $(n-2)$-Hausdorff measure of the set of singular points is zero. Moreover, $u$ is a weak solution of quasilinear system with two kinds of quadratic nonlinearities in the gradient. This is proved by a local penalty method. Bibl. – 25 titles. 
@article{ZNSL_2008_362_a1,
     author = {A. Arkhipova},
     title = {Variational problem with an obstacle in $\mathbb R^N$ for a~class of quadratic functionals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {15--47},
     publisher = {mathdoc},
     volume = {362},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a1/}
}
TY  - JOUR
AU  - A. Arkhipova
TI  - Variational problem with an obstacle in $\mathbb R^N$ for a~class of quadratic functionals
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2008
SP  - 15
EP  - 47
VL  - 362
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a1/
LA  - en
ID  - ZNSL_2008_362_a1
ER  - 
%0 Journal Article
%A A. Arkhipova
%T Variational problem with an obstacle in $\mathbb R^N$ for a~class of quadratic functionals
%J Zapiski Nauchnykh Seminarov POMI
%D 2008
%P 15-47
%V 362
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a1/
%G en
%F ZNSL_2008_362_a1
A. Arkhipova. Variational problem with an obstacle in $\mathbb R^N$ for a~class of quadratic functionals. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 39, Tome 362 (2008), pp. 15-47. http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a1/