Generalized solutions of a system of differential equations of the first order and elliptic type with discontinuous coefficients

Higher Order Sobolev-Type Spaces on the Real Line

This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces.