Iterative method for $p$-Laplacian Consider the following iterative procedure for solving the $p$-Laplace equation $\nabla \cdot (|\nabla u|^{p-2} \nabla u) = 0$ with fixed Dirichlet boundary data:


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*$u_0$ is our initial guess, for example a harmonic function.

*$u_k$ solves the equation $\nabla \cdot (|\nabla u_{k-1}|^{p-2} \nabla u_k) = 0$.


One would hope that, at least under some conditions, $u_k$ would converge to the $p$-harmonic function with the correct boundary values.
If convenient, we may assume $p > 2$ or other similar condition. $p=2$ is trivial.
This type of iteration has certainly been used to solve other nonlinear equations, so it would be a surprise if nobody had thought to use it for the $p$-Laplace equation. My questions:


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*Does this type of iterative scheme have a name or associated keywords?

*Are convergence results for this iteration and $p$-Laplace equation known? I am interested in the both the type of convergence and rate of convergence.

 A: I know this method under the name lagged diffusivity. I learned it from the paper

Vogel, Curtis R., and Mary E. Oman. "Iterative methods for total variation denoising." SIAM Journal on Scientific Computing 17.1 (1996): 227-238.

and the paper 

Chan, Tony F., and Pep Mulet. "On the convergence of the lagged diffusivity fixed point method in total variation image restoration." SIAM Journal on Numerical Analysis 36.2 (1999): 354-367.

analyzes the case $p=1$ (with additional regularization). There they write that "This idea is quite commonly used in other PDE applications,
e.g., CFD, and our theory may have applications there as well. " but I don't know more about the background. 
There are some newer paper which you find under the same buzzword, but I do not know of any papers that treat other $p$-Laplacians than $p=1$.
A: A relaxed version of this algorithm for an inhomogenous problem with $1 < p \leq 2$ is investigated by Diening, Fornasier and Wank: https://arxiv.org/abs/1702.03844
The name of the method is "Kačanov Iteration".
