Translator Disclaimer
2019 Continuity properties for divergence form boundary data homogenization problems
William M. Feldman, Yuming Paul Zhang
Anal. PDE 12(8): 1963-2002 (2019). DOI: 10.2140/apde.2019.12.1963

Abstract

We study the asymptotic behavior at rational directions of the effective boundary condition in periodic homogenization of oscillating Dirichlet data. We establish a characterization for the directional limits at a rational direction in terms of a relatively simple two-dimensional boundary layer problem for the homogenized operator. Using this characterization we show continuity of the effective boundary condition for divergence form linear systems, and for divergence form nonlinear equations we give an example of discontinuity.

Citation

Download Citation

William M. Feldman. Yuming Paul Zhang. "Continuity properties for divergence form boundary data homogenization problems." Anal. PDE 12 (8) 1963 - 2002, 2019. https://doi.org/10.2140/apde.2019.12.1963

Information

Received: 7 February 2018; Revised: 28 September 2018; Accepted: 30 November 2018; Published: 2019
First available in Project Euclid: 14 December 2019

zbMATH: 07143408
MathSciNet: MR4023973
Digital Object Identifier: 10.2140/apde.2019.12.1963

Subjects:
Primary: 35B27, 35J57, 35J60

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
40 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 8 • 2019
MSP
Back to Top