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:


1. $u\_0$ is our initial guess, for example a harmonic function.
2. $u\_k$ 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:


1. Does this type of iterative scheme have a name or associated keywords?
2. 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.



Iterative method for $p$-Laplacian
I know this method under the name *lagged diffusivity*. I learned it from the paper



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



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> 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.
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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 $p=1$.


