Abstract
Let Ω⊂Rn be a Lipschitz domain. Given 1≤p<k≤n and any u∈W2,p(Ω) belonging to the little Hölder class c1,α, we construct a sequence uj in the same space with rankD2uj<k almost everywhere such that uj→u in C1,α and weakly in W2,p. This result is in strong contrast with known regularity behavior of functions in W2,p, p≥k, satisfying the same rank inequality.
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