Regularity of homogenized boundary data in periodic homogenization of elliptic systems

Zhongwei Shen; Jinping Zhuge

doi:10.4171/JEMS/976

Regularity of homogenized boundary data in periodic homogenization of elliptic systems

Zhongwei Shen, Jinping Zhuge

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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
Pages (from-to)	2751-2776
Number of pages	26
Journal	Journal of the European Mathematical Society
Volume	32
Issue number	3
DOIs	https://doi.org/10.4171/JEMS/976
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

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10.4171/JEMS/976

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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,p for any 1 < p < ∞. In particular, this implies that the boundary layer tails are H{\"o}lder continuous of order α for any α ∈ (0, 1).",

keywords = "Boundary layers, Homogenization, Oscillating boundary data",

author = "Zhongwei Shen and Jinping Zhuge",

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: {\textcopyright} European Mathematical Society 2020.",

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AU - Zhuge, Jinping

N1 - 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.

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N2 - 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).

AB - 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).

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KW - Homogenization

KW - Oscillating boundary data

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Regularity of homogenized boundary data in periodic homogenization of elliptic systems

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Bibliographical note

Keywords

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