Journal of Mathematical Sciences

, Volume 232, Issue 3, pp 390–401 | Cite as

A Counterexample Related to the Regularity of the p-Stokes Problem

  • M. Křepela
  • M. Růžička

We construct a solenoidal vector field u belonging to \( {W}^{2,q}\left(\Omega \right)\cap {W}_0^{1,s}\left(\Omega \right),q\in \left(1,n\right),s\in \left(1,\infty \right) \), such that (1 + |Du|)p − 2, p ∈ (1, ∞), p ≠ 2, does not belong to the Muckenhoupt class A(Ω). Thus, one cannot use the Korn inequality in weighted Lebesgue spaces to prove the natural regularity of the p-Stokes problem.


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Authors and Affiliations

  1. 1.Institute of Applied MathematicsUniversity of FreiburgFreiburgGermany

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