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Uniform continuity and Brézis-Lieb-type splitting for superposition operators in Sobolev space. (English) Zbl 06992610

Summary: Using concentration-compactness arguments, we prove a variant of the Brézis-Lieb-Lemma under weaker assumptions on the nonlinearity than known before. An intermediate result on the uniform continuity of superposition operators in Sobolev space is of independent interest.

MSC:

47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
58E40 Variational aspects of group actions in infinite-dimensional spaces
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