Displaying similar documents to “The obstacle problem for functions of least gradient”

A second look on definition and equivalent norms of Sobolev spaces

Joachim Naumann, Christian G. Simader (1999)

Mathematica Bohemica

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