We consider the classical inverse mapping theorem of Nash and Moser from the angle of some recent development by Ekeland and the authors. Geometrisation of tame estimates coupled with certain ideas coming from variational analysis when applied to a directionally differentiable mapping produces very general surjectivity result and, if injectivity can be ensured, inverse mapping theorem with the expected Lipschitz-like continuity of the inverse. We also present a brief application to differential equations.

中文翻译：

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Fréchet 空间中的逆映射定理

我们从 Ekeland 和作者最近的一些发展的角度考虑 Nash 和 Moser 的经典逆映射定理。当应用于方向可微映射时，驯服估计的几何化加上来自变分分析的某些想法会产生非常普遍的满射性结果，并且如果可以确保注入性，则逆映射定理具有预期的类似 Lipschitz 的逆连续性。我们还简要介绍了微分方程的应用。