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,p for any 1 < p < ∞. In particular, this implies that the boundary layer tails are Hölder continuous of order α for any α ∈ (0, 1).
Original language | English |
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Pages (from-to) | 2751-2776 |
Number of pages | 26 |
Journal | Journal of the European Mathematical Society |
Volume | 32 |
Issue number | 3 |
DOIs | |
State | Published - Jun 2020 |
Bibliographical note
Funding Information:Acknowledgments. Research of Z. Shen was supported in part by NSF grant DMS-1600520. Research of J. Zhuge was supported in part by NSF grant DMS-1600520.
Publisher Copyright:
© European Mathematical Society 2020.
Keywords
- Boundary layers
- Homogenization
- Oscillating boundary data
ASJC Scopus subject areas
- Mathematics (all)
- Applied Mathematics