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Pointwise inequalities for Sobolev functions and some applications. (English) Zbl 0810.46030
Summary: We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer’s theorem which states that Sobolev functions can be approximated by $$\mathbb{C}^ m$$ functions both in norm and capacity.

MSC:
 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 41A80 Remainders in approximation formulas 41A63 Multidimensional problems 31B15 Potentials and capacities, extremal length and related notions in higher dimensions
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