The goal of this paper is to investigate Gevrey properties of formal solutions of certain generalized linear partial differential equations with variable coefficients. In particular, we extend the notion of moment partial differential equations to include differential operators that are not connected with kernel functions. Using the modified version of Nagumo norms and the properties of the Newton polygon we compute the Gevrey estimate for formal solutions of such generalized partial differential equations.

中文翻译：

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具有变系数的矩偏微分方程形式解的Gevrey估计。

本文的目的是研究某些变系数广义线性偏微分方程形式解的Gevrey性质。特别是，我们扩展了矩偏微分方程的概念，以包括不与核函数关联的微分算子。使用Nagumo范数的修改版本和牛顿多边形的属性，我们为此类广义偏微分方程的形式解计算了Gevrey估计。