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Continuity properties
for divergence form boundary data homogenization problems
William M. Feldman and Yuming Paul Zhang |
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Vol. 12 (2019), No. 8, 1963–2002
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Abstract |
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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. |
Keywords
homogenization, boundary layers, oscillating boundary data,
nonlinear elliptic equations, elliptic systems
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Mathematical Subject Classification 2010
Primary: 35B27, 35J57, 35J60
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Milestones
Received: 7 February 2018
Revised: 28 September 2018
Accepted: 30 November 2018
Published: 28 October 2019
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Authors |
| William M. Feldman | |
| Department of Mathematics University of Chicago Chicago, IL United States |
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| Yuming Paul Zhang | |
| Department of Mathematics University of California Los Angeles, CA United States |
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