论文标题
van der waals-cahn-hilliard方程的lusternik-schnirelman和莫尔斯理论和音量约束
Lusternik-Schnirelman and Morse theory for the Van der Waals-Cahn-Hilliard equation with volume constraint
论文作者
论文摘要
我们给出了van der waals-cahn-hilliard两相跃迁方程的解决方案的多样性结果，并在封闭的riemannian歧管上具有体积约束。我们的证明采用了经典的Lusternik-Schnirelman和Morse理论的一些结果，以及一种所谓的\ emph {Photography方法}的技术，这使我们能够根据底层折叠式的拓扑不变剂来获得解决方案数量的下限。摄影方法的设置采用了Riemannian等级的最新结果，用于少量。
We give a multiplicity result for solutions of the Van der Waals-Cahn-Hilliard two-phase transition equation with volume constraints on a closed Riemannian manifold. Our proof employs some results from the classical Lusternik--Schnirelman and Morse theory, together with a technique, the so-called \emph{photography method}, which allows us to obtain lower bounds on the number of solutions in terms of topological invariants of the underlying manifold. The setup for the photography method employs recent results from Riemannian isoperimetry for small volumes.
