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In this chapter, we provide some useful information on the function space setting, which we will require in the sequel, involving Sobolev spaces and weighted Sobolev spaces, as well as an overview of variable Sobolev spaces and an introduction to fractional Sobolev spaces. We do not give proofs, apart from some embedding theorems, for any of the results we introduce, as this section is intended to set the background for our further discussions.

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Background from Function Spaces

  • 章节

  • 发表日期：

    2026年

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  • Marek Galewski,
  • Dumitru Motreanu

摘要

In this chapter, we provide some useful information on the function space setting, which we will require in the sequel, involving Sobolev spaces and weighted Sobolev spaces, as well as an overview of variable Sobolev spaces and an introduction to fractional Sobolev spaces. We do not give proofs, apart from some embedding theorems, for any of the results we introduce, as this section is intended to set the background for our further discussions.