In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily positive) radial solutions for the Lane-Emden system posed in a ball, in the critical and supercritical regimes. Some of our results also apply to general fully nonlinear operators, such as Pucci's extremal operators, being new even for scalar equations.

中文翻译：

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一些椭圆系统的唯一延拓原理

在本文中，我们证明了一些满足合适超线性条件的椭圆偏微分方程组的独特延拓原理。作为一个应用，我们在临界和超临界状态下获得了球中的 Lane-Emden 系统不存在非平凡（不一定是正）径向解。我们的一些结果也适用于一般的完全非线性算子，例如 Pucci 的极值算子，即使对于标量方程也是新的。