用新截断法数值判定变分问题中Lavrentiev现象的存在性

Numerically Determining the Existence of Lavrentiev Phenomenon in Variational Problems by New Truncation Method

Lavrentiev现象在变分问题中是广泛存在的,严格地证明其存在性并不容易.新截断法是求解具有Lavrentiev现象的变分问题的奇性解的一种数值方法.根据新截断法的数学原理,给出了数值判定变分问题是否具有Lavrentiev现象的过程,并举出三个一维变分问题作为算例,验证了数值判定的有效性.

The Lavrentiev phenomenon in variational problems is widely existent, but it is difficult to prove its existence strictly. New Truncation Method is one kind of numerical methods which can solve the variational problems involving Lavrentiev phenomenon to get singular minimizers. According to the mathematical theory of New Truncation Method, the process of numerically determining the existence of Lavrentiev phenomenon is given in this paper. As examples, three one dimensional variational problems are listed to demonstrate the validity of numerically determining.