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

Van der Putten, Roberto

Boll. Unione Mat. Ital., VII. Ser., B 6, No. 3, 561-578 (1992).

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

Keywords:

critical values; vector valued and approximately differentiable functions; coarea formula for Sobolev functions