Christian KasselI.R.M.A. Université Louis Pasteur-C.N.R.S., 7 rue René Descartes, Strasbourg, FranceVladimir TuraevI.R.M.A. Université Louis Pasteur-C.N.R.S., 7 rue René Descartes, Strasbourg, France
We give a new characterization of the Orlicz–Sobolev space$W$^{1,Ψ}(R^{$n$}) in terms of a pointwise inequality connected to the Young function Ψ. We also study different Poincaré inequalities in the metric measure space.