Continuity Properties for Divergence Form Boundary Data Homogenization Problems

Published: January 31, 2018PDF arXiv

Abstract

We study the continuity/discontinuity of the effective boundary condition for periodic homogenization of oscillating Dirichlet data for nonlinear divergence form equations and linear systems. For linear systems we show continuity, for nonlinear equations we give an example of discontinuity.

Continuity Properties for Divergence Form Boundary Data Homogenization Problems

William M. Feldman, Yuming Paul Zhang

math.AP

Published: January 31, 2018PDF arXiv

Abstract

We study the continuity/discontinuity of the effective boundary condition for periodic homogenization of oscillating Dirichlet data for nonlinear divergence form equations and linear systems. For linear systems we show continuity, for nonlinear equations we give an example of discontinuity.