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PreprintCC BY 4.0arXiv

Quantitative periodic homogenization and uniform regularity for nonlocal equations

  • Kyeongbae Kim
  • Simon Nowak
  • Marvin Weidner
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Abstract

In this work, we study quantitative homogenization for a class of nonlocal equations with periodically oscillating Hölder continuous coefficients. For Dirichlet problems in bounded C1,α domains, we prove L2 convergence rates that are expected to be optimal. In addition, we establish interior Lipschitz estimates and optimal boundary Hölder estimates for weak solutions, with constants independent of the period of oscillation.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026quantitative,
  title = {{Quantitative periodic homogenization and uniform regularity for nonlocal equations}},
  author = {Kyeongbae Kim and Simon Nowak and Marvin Weidner},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37209},
  eprint = {2610.37209},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37209},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quantitative periodic homogenization and uniform regularity for nonlocal equations
AU  - Kyeongbae Kim
AU  - Simon Nowak
AU  - Marvin Weidner
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37209
UR  - https://arxiv.org/abs/2610.37209
AB  - In this work, we study quantitative homogenization for a class of nonlocal equations with periodically oscillating Hölder continuous coefficients. For Dirichlet problems in bounded C^1,α domains, we prove L^2 convergence rates that are expected to be optimal. In addition, we establish interior Lipschitz estimates and optimal boundary Hölder estimates for weak solutions, with constants independent of the period of oscillation.
ER  -