Title: Symmetric quadruple phase transitions

Authors: Changfeng Gui and Michelle Schatzman

Issue: Volume 57 (2008), Issue 2, 781-836

Abstract: A quadruple junction solution from $\mathbb{R}^3$ to $\mathbb{R}^3$ is constructed for a generalized Allen-Cahn equation with symmetric quadruple well potential. This solution is a three dimensional counterpart of the two dimensional triple junction solution, yet displays more complicated structure and new features. The model may be used to understand the quadruple junctions in phase separations and grain formations of crystalline materials.