TY - JOUR

T1 - Variational problem with an obstacle in RN for a class of quadratic functionals

AU - Arkhipova, A. A.

PY - 2009/6/1

Y1 - 2009/6/1

N2 - A variational problem with an obstacle for a certain class of quadratic functionals is considered. Admissible vector-valued functions are assumed to satisfy the Dirichlet boundary condition, and the obstacle is a given smooth (N∈-∈1)-dimensional surface S in R N . The surface S is not necessarily bounded. It is proved that any minimizer u of such an obstacle problem is a partially smooth function up to the boundary of a prescribed domain. It is shown that the (n∈-∈2)-Hausdorff measure of the set of singular points is zero. Moreover, u is a weak solution of a quasilinear system with two kinds of quadratic nonlinearities in the gradient. This is proved by a local penalty method. Bibliography: 25 titles.

AB - A variational problem with an obstacle for a certain class of quadratic functionals is considered. Admissible vector-valued functions are assumed to satisfy the Dirichlet boundary condition, and the obstacle is a given smooth (N∈-∈1)-dimensional surface S in R N . The surface S is not necessarily bounded. It is proved that any minimizer u of such an obstacle problem is a partially smooth function up to the boundary of a prescribed domain. It is shown that the (n∈-∈2)-Hausdorff measure of the set of singular points is zero. Moreover, u is a weak solution of a quasilinear system with two kinds of quadratic nonlinearities in the gradient. This is proved by a local penalty method. Bibliography: 25 titles.

UR - http://www.scopus.com/inward/record.url?scp=67349240813&partnerID=8YFLogxK

U2 - 10.1007/s10958-009-9452-9

DO - 10.1007/s10958-009-9452-9

M3 - Article

AN - SCOPUS:67349240813

VL - 159

SP - 391

EP - 410

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -