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The Morse-Sard theorem for Sobolev spaces in a borderline case. (English) Zbl 1251.46015

Summary: We extend the Morse-Sard theorem to mappings \(u\) belonging to the Sobolev class \(W^{n,n}(\mathbb R^{n},\mathbb R)\) with \(n\geqslant 2\) under mild regularity assumptions on the critical set of \(u\).

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
26D10 Inequalities involving derivatives and differential and integral operators
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
28A78 Hausdorff and packing measures
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