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Title: A second look on definition and equivalent norms of Sobolev spaces (English)
Author: Naumann, J.
Author: Simader, C. G.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 124
Issue: 2
Year: 1999
Pages: 315-328
Summary lang: English
Category: math
Summary: Sobolev's original definition of his spaces $L^{m,p}(\Omega)$ is revisited. It only assumed that $\Omega\subseteq\Bbb R^n$ is a domain. With elementary methods, essentially based on Poincare's inequality for balls (or cubes), the existence of intermediate derivates of functions $u\in L^{m,p}(\Omega)$ with respect to appropriate norms, and equivalence of these norms is proved. (English)
Keyword: Sobolev spaces
Keyword: Poincaré’s inequality
Keyword: existence of intermediate derivates
MSC: 46E35
idZBL: Zbl 0941.46019
idMR: MR1780700
DOI: 10.21136/MB.1999.126243
Date available: 2009-09-24T21:38:29Z
Last updated: 2020-07-29
Stable URL:
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