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Abstract 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 1p⩽2 by iteratively solving a sequence of linear elliptic problems. The algorithm can be interpreted as a relaxed Kačanov 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.
Diening et al. (Tue,) studied this question.