振荡Robin混合边值齐次化问题

Homogenization of the Oscillating Robin Mixed Boundary Value Problems

该文研究了振荡Robin混合边值齐次化问题解的收敛率.该工作的困难之处在于Robin边值上出现的振荡因子以及边界交叉项的处理.该文利用对偶方法巧妙得对振荡积分进行了估计.文中建立了解的H1和L2收敛率,所得结果明显地依赖于维数.该文可以视为将对偶方法和光滑算子,延拓到处理振荡Robin混合边值问题的情形.

In this paper,we study the convergence rates of solutions for homogenization of the oscillating Robin mixed boundary value problems.The main difficulty of this work is due to the oscillating factor on the Robin boundary as well as boundary discrepancies.Thanks to the duality approach,we could handle the oscillatory integral.As a consequence,we establish the rates of convergence in H1 and L2,which depends on the dimension explicitly.This work may be regarded as an extension of the duality approach as well as smoothing operators for oscillating Robin mixed boundary value problems.