Critical points of functionalized Lagrangians
Critical points of functionalized Lagrangians
复制标题
功能化拉格朗日量的关键点
DOI：
10.3934/dcds.2013.33.1231
复制
发表时间：
2012
影响因子：
1.1
通讯作者：
Hang Zhang
中科院分区：
文献类型：
--
作者：
K. Promislow;Hang Zhang
我们提出了一类新的高阶能量，其动力来自于对网络形成的研究。
官能化聚合物和溶剂的二元混合物。对于拉格朗日派的一大类人来说，我们
介绍它们的泛函形式，它是一种更高阶的能量平衡平方
对原始能量的变分导数。我们证明了泛函能量
在几个允许函数的自然空间上有全局极小点。关键人物
泛函拉格朗日的点包含原始拉格朗日的点，然而我们证明
对于足够的泛函强度，原始拉格朗日的所有临界点都是
泛函拉格朗日函数的鞍点，而全局极小值是一种新的结构。
We present a novel class of higher order energies motivated by the study of network formation in
binary mixtures of functionalized polymers and solvent. For a broad class of Lagrangians, we
introduce their functionalized form, which is a higher order energy balancing the square
of the variational derivative against the original energy. We show that the functionalized energies
have global minimizers over several natural spaces of admissible functions. The critical
points of the functionalized Lagrangian contain those of the original Lagrangian, however we demonstrate
that for a sufficient strength of the functionalization all the critical points of the original Lagrangian are
saddle points of the functionalized Lagrangian, and the global minima is a new structure.