Neumann边值齐次化问题:W1,p强收敛估计

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

该文研究了具有迅速振荡Neumann边值齐次化问题解的W1,p收敛率.此类问题在齐次化的高阶逼近理论中有着很重要的作用,其往往被用来描述边界分层想象.该文主要用到了解的积分表示、振荡积分估计以及周期函数Fourier展开等核心思想和技术.

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.