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Peer-reviewedCC BYJournal of Functional Analysis

Boundary regularity and Hopf lemma for nondegenerate stable operators

  • Florian Grube1
  1. 1Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany
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Abstract

We prove sharp boundary Hölder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior C 1 , Dini -property. This result is new even for the fractional Laplacian. A Hopf-type boundary lemma is proven, too. An additional feature of this work is that the regularity estimate is robust as s → 1 − and we recover the classical results for second order equations.

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Cite

BibTeXRIS
BibTeX
@article{grube2026boundary,
  title = {{Boundary regularity and Hopf lemma for nondegenerate stable operators}},
  author = {Florian Grube},
  journal = {Journal of Functional Analysis},
  year = {2026},
  month = oct,
  doi = {10.1016/j.jfa.2026.111744},
  url = {https://doi.org/10.1016/j.jfa.2026.111744},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Boundary regularity and Hopf lemma for nondegenerate stable operators
AU  - Florian Grube
PY  - 2026
DA  - 2026/10/30
JO  - Journal of Functional Analysis
DO  - 10.1016/j.jfa.2026.111744
UR  - https://doi.org/10.1016/j.jfa.2026.111744
AB  - We prove sharp boundary Hölder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior C 1 , Dini -property. This result is new even for the fractional Laplacian. A Hopf-type boundary lemma is proven, too. An additional feature of this work is that the regularity estimate is robust as s → 1 − and we recover the classical results for second order equations.
SN  - 0022-1236
SN  - 1096-0783
ER  -