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This paper is concerned with the periodic homogenization of second-order elliptic systems in divergence form with oscillating Dirichlet data or Neumann data of first order. We prove that the homogenized boundary data belongs to for any . In particular, this implies that the boundary layer tails are Hölder continuous of order for any .
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Zhongwei Shen, Jinping Zhuge, Regularity of homogenized boundary data in periodic homogenization of elliptic systems. J. Eur. Math. Soc. 22 (2020), no. 9, pp. 2751–2776DOI 10.4171/JEMS/976