One-dimensional Variational Problems
One-dimensional Variational Problems
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DOI：
10.1007/978-0-387-75934-0_6
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
G. Buttazzo;M. Giaquinta;S. Hildebrandt
中科院分区：
文献类型：
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作者：
G. Buttazzo;M. Giaquinta;S. Hildebrandt
我们现在给出几个高维变分问题的例子，这些问题使用了前几章中发展的理论。基本符号由第一章中发展的Sobolev空间提供。我们将第二章的存在性理论与第三章和第四章的近似理论结合起来，为离散化过程提供了一个完整的理论。有几个例子将在课文中充分阐述，还有几个例子在练习中找到。在本章中，我们假设域Ω是有界的。
We now give several examples of higher-dimensional variational problems that use the theory developed in previous chapters. The basic notation is provided by the Sobolev spaces developed in Chapter 1. We combine the existence theory of Chapter 2 together with the approximation theory of Chapters 3 and 4 to provide a complete theory for the discretization process. Several examples will be fully developed in the text, and several others are found in the exercises. Throughout this chapter, we assume that the domain Ω is bounded.