Annali di Matematica https://doi.org/10.1007/s10231-018-0764-6 Uniform boundary estimates in homogenization of higher-order elliptic systems 1 2 Weisheng Niu · Yao Xu Received: 2 February 2018 / Accepted: 22 May 2018 © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract This paper focuses on uniform boundary estimates in homogenization of a family of higher-order elliptic operators L , with rapidly oscillating periodic coefﬁcients. We derive m−1,λ m, p 1 uniform boundary C (0<λ< 1) and W estimates in C domains, as well as uniform m−1,1 1,θ boundary C estimate in C (0<θ < 1) domains without the symmetry assumption on the operator. The proof, motivated by the works “Armstrong and Smart in Ann Sci Éc Norm Supér (4) 49(2):423–481 (2016) and Shen in Anal PDE 8(7):1565–1601 (2015),” is based m−1 on a suboptimal convergence rate in H (). Compared to “Kenig et al. in Arch Ration Mech Anal 203(3):1009–1036 (2012)and Shen (2015),” the convergence rate obtained here does not require the symmetry assumption on the operator, nor additional assumptions on the regularity of u (the solution to the homogenized problem), and thus might be of some independent interests even for second-order elliptic
Annali di Matematica Pura ed Applicata (1923 -) – Springer Journals
Published: Jun 2, 2018
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