Homogenization of oblique boundary value problems

Sunhi Choi, Inwon C. Kim

Research output: Contribution to journalArticlepeer-review

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. While we follow the outline of Choi and Kim (Homogenization for nonlinear PDEs in general domains with oscillatory Neumann boundary data, Journal de Mathématiques Pures et Appliquées 102 (2014), no. 2, 419-448), new challenges arise due to the presence of tangential derivatives on the boundary condition in our problem. In addition, we improve and optimize the rate of convergence within our approach. Our results appear to be new even for the linear oblique problem.

Original languageEnglish (US)
Article number20220051
JournalAdvanced Nonlinear Studies
Volume23
Issue number1
DOIs
StatePublished - Jan 1 2023

Keywords

  • elliptic operator
  • homogenization
  • oblique boundary problem

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • General Mathematics

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