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A note on the monotonicity formula of Caffarelli–Jerison–Kenig

A note on the monotonicity formula of Caffarelli–Jerison–Kenig

The aim of this note is to prove the monotonicity formula of Caffarelli–Jerison–Kenig for functions, which are not necessarily continuous. We also give a detailed proof of the multiphase version of the monotonicity formula in any dimension.