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

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Variational problem with an obstacle in R^N for a class of quadratic functionals. / Arkhipova, A. A.

In: Journal of Mathematical Sciences , Vol. 159, No. 4, 01.06.2009, p. 391-410.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{fbf4ead711f54ab2b8a5e8fb08ead577,

title = "Variational problem with an obstacle in RN for a class of quadratic functionals",

abstract = "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.",

author = "Arkhipova, {A. A.}",

year = "2009",

month = jun,

day = "1",

doi = "10.1007/s10958-009-9452-9",

language = "English",

volume = "159",

pages = "391--410",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "4",

}

RIS

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 -

ID: 51917804