Abstract

We prove a version of the negative norm theorem in Orlicz–Sobolev spaces. A study of boundedness properties of the Bogovskiĭ operator between Orlicz spaces is a crucial step, of independent interest, in our approach. Applications to the problem of pressure reconstruction for non-Newtonian fluids governed by constitutive laws, which are not necessarily of power type, are presented. A key inequality for a numerical analysis of the underlying elliptic system is also derived.

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