Pith Number

pith:YXSOGT3C

pith:2026:YXSOGT3CYAQKUWGRF5JYHN4NAH

not attested not anchored not stored refs resolved

Optimal stability of complement value problems for p-L\'evy operators

Guy Foghem

Solutions to p-Lévy integro-differential equations converge strongly to local p-Laplacian limits in the optimal Sobolev norm as the nonlocality parameter s approaches 1 from below.

arxiv:2605.13389 v1 · 2026-05-13 · math.AP

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\usepackage{pith}
\pithnumber{YXSOGT3CYAQKUWGRF5JYHN4NAH}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

under suitable assumptions on Ω, f_s and g_s, we show that (u_s)_s strongly converges as s → 1^- in the optimal, that is, ||u_s - u_1||_{W^{s,p}(Ω)} → 0

C2weakest assumption

Suitable assumptions on the domain Ω, the right-hand sides f_s, and the boundary data g_s that allow the nonlocal-to-local passage; the precise regularity or compatibility conditions on these data are not detailed in the abstract.

C3one line summary

Solutions to fractional p-Laplacian equations converge optimally in W^{s,p} to local p-Laplacian solutions as s approaches 1.

References

57 extracted · 57 resolved · 0 Pith anchors

[1] R. Adams, N. Aronszajn, and K. T. Smith. Theory of Bessel pot entials. II. Ann. Inst. Fourier (Grenoble), 17(fasc. 2):1–135, 1967 1967

[2] F. Andreu, J. M. Maz´ on, J. D. Rossi, and J. Toledo. A nonlocal p-Laplacian evolution equation with Neumann boundary conditions. J. Math. Pures Appl. (9) , 90(2):201–227, 2008 2008

[3] Maz´ on, Julio D 2010

[4] Bourgain-Bre zis-Mironescu domains 2020

[5] Bellido and Alejandro Ortega 2021

Receipt and verification

First computed	2026-05-18T02:44:47.728161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5e4e34f62c020aa58d12f5383b78d01c7f7e288a60730e426fcd6753b0648c2

Aliases

arxiv: 2605.13389 · arxiv_version: 2605.13389v1 · doi: 10.48550/arxiv.2605.13389 · pith_short_12: YXSOGT3CYAQK · pith_short_16: YXSOGT3CYAQKUWGR · pith_short_8: YXSOGT3C

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YXSOGT3CYAQKUWGRF5JYHN4NAH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c5e4e34f62c020aa58d12f5383b78d01c7f7e288a60730e426fcd6753b0648c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24ff752d0fd8359c9476896a5b240810c072bff8310fbeababbf25591a3503c6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T11:46:54Z",
    "title_canon_sha256": "b45f2c94d902325197dc6b15369b20d2571ce0788bf527d47aaaa5aaf3acfb4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13389",
    "kind": "arxiv",
    "version": 1
  }
}