Addendum to Article “A Counterexample Related to the Regularity of the p-Stokes Problem”

Abstract

We show existence of a solenoidal vector field u belonging to $$ {W}^{2,q}\left(\Omega \right)\cap {W}_0^{1,s}\left(\Omega \right), $$ s ∈ (1,∞), q ∈ (1, n), such that (δ+|Du|)p−2, p ∈ (1, 2)∪(2,∞), δ ∈ [0, 1], does not belong to the Muckenhoupt class A∞(Ω). This is an extension of our result in [1] proved for δ = 1.