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Hölder type quasicontinuity. (English) Zbl 0803.46037

Summary: It is proved that a function \(u\in L^{m,p}(\mathbb{R}^ n)\) (which coincides with the Sobolev space \(W^{1,p}(\mathbb{R}^ n)\) if \(m=1\)) coincides with a Hölder continuous function \(w\) outside a set of small \(m\), \(q\)-capacity, where \(q< p\). Moreover, if \(m=1\), then the function \(w\) can be chosen to be close to \(u\) in the \(W^{1,p}\)-norm.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
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