Open Research Index

Boundary regularity for non-local operators with symmetric kernels and vanishing horizon

Philipp Svinger

Palomar Registrypalomar/PALOMAR-2026-09-15-000001Sep 15, 2026math.APscore 0

This Lean 4 formalization proves the two main theorems of the paper 'Boundary regularity for non-local operators with symmetric kernels and vanishing horizon' (arXiv:2504.00567v1). For a fractional order s in (1/2,1), the paper studies a nonlocal operator with symmetric kernel whose interaction horizon depends on the distance to the boundary and on a horizon parameter sigma in (0,1], and shrinks near the boundary. The formalization proves that weak solutions u to the Dirichlet problem with zero Dirichlet data and bounded right-hand side are in the Hölder space C^{2s-1} up to the boundary.…

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-09-15-000001
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-15-000001/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-15-000001/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'