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On Hardy-type inequalities. (English) Zbl 0915.46027

Let \(D\) be a domain in \(\mathbb{R}^n\) and let \(d(x)\) be the distance of \(x\in D\) to the boundary \(\partial D\). The paper deals with Hardy inequalities of type \[ \int_D d(x)^{-p\alpha}| u(x)|^p dx\leq c\int_D d(x)^{-p\beta}| \nabla u(x)|^p dx \] for compactly supported \(C^1\)-functions in \(D\). These inequalities are studied under weak assumptions for \(D\): plump domains, John domains, domains with finite width etc.
Reviewer: H.Triebel (Jena)

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
26D10 Inequalities involving derivatives and differential and integral operators

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References:

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