A counterexample related to the regularity of the $p$-Stokes problem

Martin Křepela, Michael Růžička

In this paper we construct a solenoidal vector field $\mathbf{u}$ belonging to $W^{2,q}(\Omega )\cap W_0^{1,s}(\Omega )$, $s\in (1,\infty )$, $q\in (1,n)$, such that $(1+|\mathbf{Du}|{)}^{p-2}$…