A Relaxed Kačanov Iteration for the $p$-Poisson Problem

Diening L, Fornasier M, Wank M. A Relaxed Kačanov Iteration for the $p$-Poisson Problem. arXiv:1702.03844. 2017.In this paper, we introduce an iterative linearization scheme that allows to approximate the weak solution of the $p$-Poisson problem \begin{align*} -\operatorname{div}(|\nabla u|^{p-2}\nabla u) &= f\quad\text{in }\Omega, u&= 0\quad\text{on}\partial\Omega \end{align*} for $1 < p \leq 2$. The algorithm can be interpreted as a relaxed Ka\v{c}anov iteration. We prove that the algorithm converges at least with an algebraic rate