A Relaxed Kačanov iteration for the p-poisson problem

In this paper we introduce and analyze an iteratively re-weighted algorithm, that allows to approximate the weak solution of the p-Poisson problem for $$1 < p \leqslant 2$$ by iteratively solving a sequence of linear elliptic problems. The algorithm can be interpreted as a relaxed Kacanov iteration, as so-called in the specific literature of the numerical solution of quasi-linear equations. The main contribution of the paper is proving that the algorithm converges at least with an algebraic rate.

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