Abstract
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.
| 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 H01-function. / Idogawa, Tomoyuki.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 47, No. 4, 08.2001, p. 2863-2868.Research output: Contribution to journal › Article
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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 -