Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4611380 | Journal of Differential Equations | 2013 | 12 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hayk Aleksanyan, Henrik Shahgholian, Per Sjölin,