JournalsjemsVol. 22, No. 9pp. 2751–2776

Regularity of homogenized boundary data in periodic homogenization of elliptic systems

  • Zhongwei Shen

    University of Kentucky, Lexington, USA
  • Jinping Zhuge

    University of Kentucky, Lexington, USA and University of Chicago, USA
Regularity of homogenized boundary data in periodic homogenization of elliptic systems cover
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Abstract

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 W1,pW^{1, p} for any 1<p<1 < p < \infty. In particular, this implies that the boundary layer tails are Hölder continuous of order α\alpha for any α(0,1)\alpha \in (0,1).

Cite this article

Zhongwei Shen, Jinping Zhuge, Regularity of homogenized boundary data in periodic homogenization of elliptic systems. J. Eur. Math. Soc. 22 (2020), no. 9, pp. 2751–2776

DOI 10.4171/JEMS/976