We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex embeddings of hypersurfaces, differential forms, and lapse functions in Lorentzian geometry.

中文翻译：

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开放偏微分关系的局部灵活性

我们表明，开放偏微分关系的解的局部变形（接近闭合子集）可以扩展到全局变形，前提是除了最高导数之外的所有变形沿子集保持不变。这个一般结果的适用性通过一些例子来说明，处理洛伦兹几何中超曲面、微分形式和失效函数的凸嵌入。