Approximation by mappings with singular Hessian minors. (November 2018)

• Record Type: Journal Article
• Authors: Liu, Zhuomin; Malý, Jan; Pakzad, Mohammad Reza
• Is Part Of: Nonlinear analysis. Volume 176(2018)
• Page Start: 209
• Page End: 225
• Publication Date: 2018-11
• Subjects: Monge–Ampère equation -- Nonlinear approximation -- Hessian minors; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.06.015
• Languages: English
• ISSNs: 0362-546X

Abstract

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.