Abstract This paper presents some computer-assisted procedures to prove the invertibility of a second-order linear elliptic operator and to compute a bound for the norm of its inverse. These approaches are based on constructive L 2 -norm estimates of the Laplacian and improve on previous procedures that use projection and a priori error estimations. Several examples which confirm the actual effectiveness of the procedures are reported.

中文翻译：

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二阶线性椭圆算子可逆性验证的一些改进

摘要 本文提出了一些计算机辅助程序来证明二阶线性椭圆算子的可逆性并计算其逆范数的界限。这些方法基于拉普拉斯算子的建设性 L 2 -范数估计，并改进了先前使用投影和先验误差估计的程序。报告了几个证实程序实际有效性的例子。