### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 2863-2868 |

Number of pages | 6 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 47 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2001 Aug |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Mathematics(all)

### Cite this

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

Research output: Contribution to journal › Article

_{0}

^{1}-function',

*Nonlinear Analysis, Theory, Methods and Applications*, vol. 47, no. 4, pp. 2863-2868. https://doi.org/10.1016/S0362-546X(01)00406-0

}

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 -