Uniform Continuity and Br\'ezis-Lieb Type Splitting for Superposition   Operators in Sobolev Space
  Using concentration-compactness arguments we prove a variant of the Brezis-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. 
Nils Ackermann
math.FA math.AP