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Some Basic Properties of Sobolev Spaces
Abstract In the modern theory of partial differential equations, the smoothness of solutions is commonly described in terms of Sobolev spaces. They have nearly become the basic language of PDE. Detailed studies of Sobolev spaces can be found in [2, 138], for example. In this section, we will briefly introduce what these spaces are and some of their basic properties, to the extent that they are sufficient for the subsequent material in this book. The most important thing here is to understand the content of Theorems 2.1, 2.2 and 2.8 in this chapter. Their proofs, although not difficult to comprehend, do appear a little technical for an inexperienced reader and, thus, can be put off to the second reading.
Some Basic Properties of Sobolev Spaces
Abstract In the modern theory of partial differential equations, the smoothness of solutions is commonly described in terms of Sobolev spaces. They have nearly become the basic language of PDE. Detailed studies of Sobolev spaces can be found in [2, 138], for example. In this section, we will briefly introduce what these spaces are and some of their basic properties, to the extent that they are sufficient for the subsequent material in this book. The most important thing here is to understand the content of Theorems 2.1, 2.2 and 2.8 in this chapter. Their proofs, although not difficult to comprehend, do appear a little technical for an inexperienced reader and, thus, can be put off to the second reading.
Some Basic Properties of Sobolev Spaces
Chen, Goong (author) / Zhou, Jianxin (author)
2010-01-01
15 pages
Article/Chapter (Book)
Electronic Resource
English
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