Scholarlink

Chapter 5 is a brief introduction to function spaces such as Hölder, Sobolev and Besov spaces. We treat the following function spaces that enter naturally in connection with elliptic boundary value problems: In particular, we formulate the imbedding characteristics of Sobolev spaces and the Rellich–Kondrachov compactness theorem for Sobolev spaces that render these spaces so useful in the study of elliptic boundary value problems. It should be emphasized that Triebel (1983) and Franke–Runst (1995) studied regular elliptic boundary value problems in the framework of Besov spaces \(B^{s}_{p,q}\) and Triebel–Lizorkin spaces \(F^{s}_{p,q}\) .

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Elements of Function Spaces

  • 章节

  • 发表日期：

    2025年

查看全文
  • Kazuaki Taira

摘要

Chapter 5 is a brief introduction to function spaces such as Hölder, Sobolev and Besov spaces. We treat the following function spaces that enter naturally in connection with elliptic boundary value problems: In particular, we formulate the imbedding characteristics of Sobolev spaces and the Rellich–Kondrachov compactness theorem for Sobolev spaces that render these spaces so useful in the study of elliptic boundary value problems. It should be emphasized that Triebel (1983) and Franke–Runst (1995) studied regular elliptic boundary value problems in the framework of Besov spaces \(B^{s}_{p,q}\) and Triebel–Lizorkin spaces \(F^{s}_{p,q}\) .