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PreprintCC BY-NC-ND 4.0arXiv

Boundary pointwise regularity for the p-Laplace equation on C1,Dini domains

  • Xuemei Li
  • Yuanyuan Lian
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Abstract

This paper investigates the boundary pointwise regularity of solutions to the p-Laplace equation. By treating curved boundaries as perturbations of flat ones, we establish the boundary pointwise Lipschitz regularity under the exterior C1,Dini condition and the Hopf lemma under the interior C1,Dini condition. We also establish the boundary pointwise C1 regularity under the C1,Dini condition by a compactness argument.

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Cite

BibTeXRIS
BibTeX
@misc{li2026boundary,
  title = {{Boundary pointwise regularity for the $p$-Laplace equation on $C^1,\mathrmDini$ domains}},
  author = {Xuemei Li and Yuanyuan Lian},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33577},
  eprint = {2609.33577},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33577},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Boundary pointwise regularity for the p-Laplace equation on C^1,Dini domains
AU  - Xuemei Li
AU  - Yuanyuan Lian
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33577
UR  - https://arxiv.org/abs/2609.33577
AB  - This paper investigates the boundary pointwise regularity of solutions to the p-Laplace equation. By treating curved boundaries as perturbations of flat ones, we establish the boundary pointwise Lipschitz regularity under the exterior C^1,Dini condition and the Hopf lemma under the interior C^1,Dini condition. We also establish the boundary pointwise C^1 regularity under the C^1,Dini condition by a compactness argument.
ER  -