Convergence rates in homogenization of p-Laplace equations

• Main Authors: Jie Zhao, Juan Wang
• Format: Article
• Language: English
• Published: SpringerOpen 2019-08-01
• Series: Boundary Value Problems
• Subjects: Homogenization; Convergence rates; p-Laplace equations; Oscillating
• Online Access: http://link.springer.com/article/10.1186/s13661-019-1258-1

Abstract This paper is concerned with homogenization of p-Laplace equations with rapidly oscillating periodic coefficients. The main difficulty of this work is due to the nonlinear structure in this field concerning p-Laplace equations itself. Utilizing the layer and co-layer type estimates as well as homogenization techniques, we establish the desired error estimates. As a consequence, we obtain the rates of convergence for solutions in W01,p $W_{0}^{1,p}$ as well as Lp $L^{p}$. Meanwhile, our convergence rate results do not involve the higher derivatives any more. This may be viewed as rather surprising. The novelty of this work is that it seems to find a new analysis method in quantitative homogenization.