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.


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