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

Da Lio, Francesca; Lions, Pierre-Louis; Barles, Guy; Souganidis, Panagiotis E. (2008), Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions, Indiana University Mathematics Journal, 57, p. 2355-2376

Type
Article accepté pour publication ou publié
Date
2008
Journal name
Indiana University Mathematics Journal
Volume
57
Publisher
Department of Mathematics
Pages
2355-2376
Metadata
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Author(s)
Da Lio, Francesca

Lions, Pierre-Louis

Barles, Guy

Souganidis, Panagiotis E.
Abstract (EN)
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.
Subjects / Keywords
PDEs; fully nonlinear equations