Iteration algorithm for a certain projection of H₀¹-function

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_Ku from each given u ∈ V. In this article, an iterative method to approximate P_Ku for V = H₀/¹(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.