Affiliations: Laboratoire de Mathématiques et Physique Théorique, Fédération Denis Poisson, Faculté des Sciences et Techniques, Université de Tours, Tours, France | Institut Camille Jordan, Université de Lyon, Ecole Centrale de Lyon, Ecully, France
Note: [] Corresponding author: Elisabeth Mironescu, Institut Camille Jordan, Université de Lyon, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France. Tel.: +33 4 72 44 62 75; Fax: +33 4 72 43 16 87; E-mail: [email protected]
Abstract: We study two types of asymptotic problems whose common feature – and difficulty – is to exhibit oscillating Dirichlet boundary conditions: the main contribution of this article is to show how to recover the Dirichlet boundary condition for the limiting equation. These two types of problems are (i) periodic homogenization problems for fully nonlinear, second-order elliptic partial differential equations set in a half-space and (ii) parabolic problems with an oscillating in time Dirichlet boundary condition. In order to obtain the Dirichlet boundary condition for the limiting problem, the key step is a blow-up argument near the boundary which leads to the study of Dirichlet problems set on half-space type domains and of the asymptotic behavior of the solutions when the distance to the boundary tends to infinity.
