We give two short and elementary proofs of a characterization of constants function by Brezis. Whereas the original proof involves some refined arguments on Sobolev spaces and BV functions, ours are based either on convolutions or on a sort of nonsmooth Mean Value Theorem which is new to our knowledge.
An elementary proof of a characterization of constant functions
DE MARCO, GIUSEPPE;MARICONDA, CARLO;
2008
Abstract
We give two short and elementary proofs of a characterization of constants function by Brezis. Whereas the original proof involves some refined arguments on Sobolev spaces and BV functions, ours are based either on convolutions or on a sort of nonsmooth Mean Value Theorem which is new to our knowledge.
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