Uniform Continuity and Br\'ezis-Lieb Type Splitting for Superposition Operators in Sobolev Space
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math.AP
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continuityoperatorssobolevspacesuperpositionuniformargumentsassumptions
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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.
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