The paper is devoted to the classification of entire solutions to the Cahn–Hilliard equation \(-\Delta u=u-u^3-\delta \) in \(\mathbb {R}^N\), with particular interest in those solutions whose nodal set is either bounded or contained in a cylinder. The aim is to prove either radial or cylindrical symmetry, under suitable hypothesis.

中文翻译：

---

Cahn-Hilliard方程解的径向和圆柱对称

纸张被专门项的Cahn-Hilliard方程整个解决方案的分类\（ - \德尔塔U = UU ^ 3- \增量\）在\（\ mathbb {R} ^ N \） ，在这些解决方案特别感兴趣其节点集有界或包含在圆柱体中。目的是在适当的假设下证明径向或圆柱对称。