Homogenization of the Oscillating Dirichlet Boundary Condition in\n General Domains

2013/03/07 by William M. Feldman, Feldman, William M., W. M. Feldman
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1303.1854

openalex publication_date 2013/03/07 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

We prove the homogenization of the Dirichlet problem for fully nonlinear\nelliptic operators with periodic oscillation in the operator and of the\nboundary condition for a general class of smooth bounded domains. This extends\nthe previous results of Barles and Mironescu in half spaces. We show that\nhomogenization holds despite a possible lack of continuity in the homogenized\nboundary data. The proof is based on a comparison principle with partial\nDirichlet boundary data which is of independent interest.\n

Related

• Homogenization of fully nonlinear elliptic equations with oscillating dirichlet boundary data
• On homogenization problems for fully nonlinear equations with oscillating Dirichlet boundary conditions
• Homogenization and boundary layers in domains of finite type
• Recent progress in the theory of homogenization with oscillating\n Dirichlet data
• Homogenization of a locally periodic oscillating boundary