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On the critical values lemma and the coarea formula. (Italian. English summary) Zbl 0762.46019

Summary: We prove the critical values lemma in the case of vector valued and approximately differentiable functions and the validity of the coarea formula for Sobolev functions \(W^{1,p}(\Omega;\mathbb{R}^ m)\) with \(p\) large enough.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46G05 Derivatives of functions in infinite-dimensional spaces
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
49J27 Existence theories for problems in abstract spaces
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