### 抄録

The projection mapping P_{K}: V → K plays an important role in the treatment of variational inequalities, where V is some Hilbert space and K is a certain closed convex subset of V. But, only for few problems, it is known how to get or approximate the explicit form of P_{K}u from each given u ∈ V. In this article, an iterative method to approximate P_{K}u for V = H_{0}/^{1}(a, b) and K = {f ∈ V; |∇f| ≤ 1 a.e.} is proposed. This P_{K} is related to the elasto-plastic torsion problems. Moreover, an expansion of the method for higher dimensional but radial symmetric case is shown.

元の言語 | English |
---|---|

ページ（範囲） | 2863-2868 |

ページ数 | 6 |

ジャーナル | Nonlinear Analysis, Theory, Methods and Applications |

巻 | 47 |

発行部数 | 4 |

DOI | |

出版物ステータス | Published - 2001 8 |

### Fingerprint

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Mathematics(all)

### これを引用

**Iteration algorithm for a certain projection of H _{0}^{1}-function.** / Idogawa, Tomoyuki.

研究成果: Article

}

TY - JOUR

T1 - Iteration algorithm for a certain projection of H01-function

AU - Idogawa, Tomoyuki

PY - 2001/8

Y1 - 2001/8

N2 - The projection mapping PK: V → K plays an important role in the treatment of variational inequalities, where V is some Hilbert space and K is a certain closed convex subset of V. But, only for few problems, it is known how to get or approximate the explicit form of PKu from each given u ∈ V. In this article, an iterative method to approximate PKu for V = H0/1(a, b) and K = {f ∈ V; |∇f| ≤ 1 a.e.} is proposed. This PK is related to the elasto-plastic torsion problems. Moreover, an expansion of the method for higher dimensional but radial symmetric case is shown.

AB - The projection mapping PK: V → K plays an important role in the treatment of variational inequalities, where V is some Hilbert space and K is a certain closed convex subset of V. But, only for few problems, it is known how to get or approximate the explicit form of PKu from each given u ∈ V. In this article, an iterative method to approximate PKu for V = H0/1(a, b) and K = {f ∈ V; |∇f| ≤ 1 a.e.} is proposed. This PK is related to the elasto-plastic torsion problems. Moreover, an expansion of the method for higher dimensional but radial symmetric case is shown.

UR - http://www.scopus.com/inward/record.url?scp=0035420995&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035420995&partnerID=8YFLogxK

U2 - 10.1016/S0362-546X(01)00406-0

DO - 10.1016/S0362-546X(01)00406-0

M3 - Article

AN - SCOPUS:0035420995

VL - 47

SP - 2863

EP - 2868

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 4

ER -