Article ID Journal Published Year Pages File Type
4611380 Journal of Differential Equations 2013 12 Pages PDF
Abstract

In this paper we prove convergence results for homogenization problem for solutions of partial differential system with rapidly oscillating Dirichlet data. Our method is based on analysis of oscillatory integrals. In the uniformly convex and smooth domain, and smooth operator and boundary data, we prove pointwise convergence results, namely|uε(x)−u0(x)|⩽Cκε(d−1)/21d(x)κ,∀x∈D,∀κ>d−1, where uεuε and u0u0 are solutions of respectively oscillating and homogenized Dirichlet problems, and d(x)d(x) is the distance of x from the boundary of D  . As a corollary for all 1⩽p<∞1⩽p<∞ we obtain LpLp convergence rate as well.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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