Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1115-1124.

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Homogenization of the Neumann Boundary Value Problem: The Sharper W1,p Estimate

Wang Juan, Zhao Jie   

  1. College of Science, Zhongyuan University of Technology, Zhengzhou 451191
  • Received:2018-11-23 Revised:2019-02-27 Published:2019-11-08
  • Supported by:
    Supported by the NSFC (11626239), the Education Department of Henan Province (18A110037) and the CSC (201708410483)

Abstract: In this paper, we shall strengthen our results on the W1,p convergence rates for homogenization problems for solutions of partial differential equations with rapidly oscillating Neumann boundary data. Such a problem raised due to its importance for higher order approximation in homogenization theory, which gives rise to the so-called boundary layer phenomenon. Our techniques are based on integral representation of the solutions as well as analysis of oscillatory integrals, in conjunction with Fourier expansion of the oscillating periodic function.

Key words: Homogenization, Convergence rates, Oscillating, Neumann functions

CLC Number: 

  • O175.23
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