Homogenization of oblique boundary value problems

2019/11/15 by Sunhi Choi, Choi, Sunhi, Inwon C. Kim +1
Computer Science · Engineering · Mathematics · #35J60 #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.1911.06909

openalex publication_date 2019/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a nonlinear Neumann problem, with periodic oscillation in the elliptic operator and on the boundary condition. Our focus is on problems posed in half-spaces, but with general normal directions that may not be parallel to the directions of periodicity. As the frequency of the oscillation grows, quantitative homogenization results are derived. When the homogenized operator is rotation-invariant, we prove the Hölder continuity of the homogenized boundary data.

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