We present a class of models of elastic phase transitions with incompatible energy wells in an arbitrary space dimension, where in a hard device an abundance of Lipschitz global minimizers coexists with a complete lack of strong local minimizers. The analysis is based on the proof that every strong local minimizer in a hard device is also a global minimizer which is applicable much beyond the chosen class of models. Along the way we show that a new demonstration of sufficiency for a subclass of affine boundary conditions can be built around a novel nonlinear generalization of the classical Clapeyron theorem.

中文翻译：

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一类没有局部但有多个全局极小化器的非线性弹性问题

我们提出了一类在任意空间维度上具有不相容能量井的弹性相变模型，其中在硬设备中，大量 Lipschitz 全局最小化器与完全缺乏强局部最小化器共存。该分析基于以下证据：硬设备中的每个强局部最小化器也是全局最小化器，其适用范围远远超出所选模型类别。在此过程中，我们证明了仿射边界条件子类的充分性的新证明可以围绕经典克拉佩龙定理的新颖非线性推广来构建。