与二次双阱能量相关的非凸极小化——通过凸问题的逼近
泛函分析
2016-08-14 v2
摘要
研究了一种表示为两个二次函数（称为相能量）的最小值的双阱能量，并考虑了相应积分泛函的极小化。由于该积分不是序列弱下半连续的，因此不存在经典极小元。为了推导下确界的松弛公式，构造了一个由适当逼近原始非凸问题的凸问题的解组成的极小化序列。该序列的弱极限、相应对偶问题解序列的弱极限以及与相能量相关的特征函数的弱极限均包含在松弛公式中。
引用
@article{arxiv.0907.1120,
title = {Nonconvex minimization related to quadratic double-well energy - approximation by convex problems},
author = {Zdzisław Naniewicz and Piotr Puchała},
journal= {arXiv preprint arXiv:0907.1120},
year = {2016}
}
备注
21 pages; This article has been published after the death of Professor Z. Nanieiwcz. Version published in C&C (see Journal Reference below) differs from the one uploaded above, due to the reviewers' remarks. I have decided to correct typos and omissions only, to preserve the original form of the article as seen by Professor Naniewicz