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arXiv · 1907.08112

Symmetry of constrained minimizers of the Cahn-Hilliard energy on the torus

Michael Gelantalis·Alfred Wagner·Maria G. Westdickenberg
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Abstract

We establish sufficient conditions for a function on the torus to be equal to its Steiner symmetrization and apply the result to volume-constrained minimizers of the Cahn-Hilliard energy. We also show how two-point rearrangements can be used to establish symmetry for the Cahn-Hilliard model. In two dimensions, the Bonnesen inequality can then be applied to quantitatively estimate the sphericity of superlevel sets.

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Michael Gelantalis, Alfred Wagner, Maria G. Westdickenberg. 2019-07-18. Symmetry of constrained minimizers of the Cahn-Hilliard energy on the torus. https://arxiv.org/abs/1907.08112

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