Approximation by mappings with singular Hessian minors. (November 2018) - Liu, Zhuomin; Malý, Jan; Pakzad, Mohammad Reza
Abstract: Let Ω ⊂ R n be a Lipschitz domain. Given 1 ≤ p < k ≤ n and any u ∈ W 2, p ( Ω ) belonging to the little Hölder class c 1, α, we construct a sequence u j in the same space with rank D 2 u j < k almost everywhere such that u j → u in C 1, α and weakly in W 2, p . This result is in strong contrast with known regularity behavior of functions in W 2, p, p ≥ k, satisfying the same rank inequality.