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arXiv · 2301.01870

A class of nonlinear elasticity problems with no local but many global minimizers

Yury Grabovsky·Lev Truskinovsky
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Abstract

We present a class of models of elastic phase transitions with incompatible energy wells in any space dimension, where an abundance of Lipschitz global minimizers in a hard device coexists with a complete lack of strong local minimizers. The analysis hinges 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 proof of sufficiency for a subclass of affine boundary conditions can be built around a novel nonlinear generalization of the classical Clapeyron theorem, whose subtle relation to dynamics was studied extensively by R. Fosdick.

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Yury Grabovsky, Lev Truskinovsky. 2023-01-05. A class of nonlinear elasticity problems with no local but many global minimizers. https://arxiv.org/abs/2301.01870

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