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A second look on definition and equivalent norms of Sobolev spaces

Joachim NaumannChristian G. Simader — 1999

Mathematica Bohemica

Sobolev’s original definition of his spaces L m , p ( Ω ) is revisited. It only assumed that Ω 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 L m , p ( Ω ) with respect to appropriate norms, and equivalence of these norms is proved.

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