Structure of stable solutions of a one-dimensional variational problem
Structure of stable solutions of a one-dimensional variational problem
复制标题
一维变分问题稳定解的结构
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
N. Yip
中科院分区：
文献类型：
--
作者：
N. Yip
对于一维高阶变分问题，我们证明了所有具有低能量的h2 -局部极小值的周期性。这些结果扩展和补充了Stefan Muller关于全局极小器结构的早期工作。本工作中所研究的能量泛函是由对相干固相转变的研究以及正则化和小尺度结构形成的影响之间的竞争所激发的。在特殊选择双线性双阱势函数的情况下，我们利用显式解公式来分析相界之间复杂的相互作用。我们的分析可以为解决一般势函数的问题提供见解。
We prove the periodicity of all H 2 -local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Muller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double well potential function, we make use of explicit solution formulas to analyze the intricate interactions between the phase boundaries. Our analysis can provide insights for tackling the problem with general potential functions.