Optimal Shape Design, Lecture Notes in Maths. 1740, A. Cellina & A. Ornelas eds, 47{156, Springer, 2000. An Introduction to the Homogenization Method in Optimal Design
Optimal Shape Design, Lecture Notes in Maths. 1740, A. Cellina & A. Ornelas eds, 47{156, Springer, 2000. An Introduction to the Homogenization Method in Optimal Design
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DOI：
10.1007/bfb0106742
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发表时间：
2000
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影响因子：
--
通讯作者：
L. Tartar
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作者：
L. Tartar
本课程介绍了导致同质化问题的优化/优化设计问题，以及弗朗索瓦·木拉提和我在70年代开发的处理这些问题的方法。我采用了一个按时间顺序的观点，我认为这种观点最适合描述一些新的技术(现在经常被错误地归因于)是如何被引入来克服我们遇到的一些困难，或者是为了概括我们在搜索中发现的有用的特定结果。在数学研究中有很多方法，我希望对我们在新问题面前思考方式的描述可以帮助一些人自己体验发现的非凡感觉；然而，必须说，一个人很少发现自己处于别人以前经历过的完全相同的情况。一个人的发现可能也为其他人所知，这一事实是Ennio de Giorgi在《chi cerca trova，chi ricerca ritrova》1中恢复的。
This course describes Optimization/Optimal Design problems which lead to Homogenization questions, together with the method to treat them that Francois MURAT and I had developed, mostly in the 70s. I adopt a chronological point of view, which I find best for describing how some new techniques (which are often misattributed nowadays) were introduced for overcoming some difficulties that we had encountered, or for generalizing a particular result that we had found useful in our search.There are many ways to practice research in Mathematics, and I hope that the description of the way we thought in front of new questions could help some to experience for themselves the extraordinary feeling of discovery; it must be said, however, that one rarely finds oneself in exactly the same situations that others had experienced before. What one finds may also have been known to others, a fact that Ennio DE GIORGI had resumed in" Chi cerca trova, chi ricerca ritrova" 1.