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, G.; Mariconda, C.; Solimini, Sergio Fausto. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - STAMPA. - 8:3(2008), pp. 597-602. [10.1515/ans-2008-0306]
An elementary proof of a characterization of constant functions
SOLIMINI, Sergio Fausto
2008-01-01
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.File in questo prodotto:
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