Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions

Details Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions

2009-10-25

arxiv.org/abs/0910.4720v1

Indiana University Mathematics Journal 57, 5 (2008) 2355--2376

Mathematics

Analysis of PDEs

Scientific paper

We study periodic homogenization problems for second-order pde in half-space type domains with Neumann boundary conditions. In particular, we are interested in "singular problems" for which it is necessary to determine both the homogenized equation and boundary conditions. We provide new results for fully nonlinear equations and boundary conditions. Our results extend previous work of Tanaka in the linear, periodic setting in half-spaces parallel to the axes of the periodicity, and of Arisawa in a rather restrictive nonlinear periodic framework. The key step in our analysis is the study of associated ergodic problems in domains with similar structure.

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