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 $1 < p \leq 2$ by iteratively solving a sequence of linear elliptic problems. The algorithm can be interpreted as a relaxed Ka{\v c}anov 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.

翻译：在本文中,我们引入并分析了一种迭代的重新加权算法,这种算法能够通过迭代解决一系列线性椭圆形问题,以1美元 < p\leq 2美元来将美元-Poisson问题的微弱解决办法近似于1美元 < p\leq 2美元。这种算法可以被解释为放松的Ka{v c}anov迭代,这在准线性方程式数字解算法的具体文献中是所谓的。论文的主要贡献是证明该算法至少与代数率一致。