Pith Number

pith:FP3AG7DG

pith:2026:FP3AG7DGIRCWYJ3L3HZWTWEWV7

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Regularity of superposition operators of mixed fractional order

R. Lakshmi, Sekhar Ghosh, Souvik Bhowmick, Vishvesh Kumar

Weak solutions to mixed local-nonlocal fractional superposition operators are locally Hölder continuous.

arxiv:2605.15346 v1 · 2026-05-14 · math.AP

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Record completeness

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Claims

C1strongest claim

We establish the local Hölder continuity of weak solutions, the weak Harnack inequality for weak supersolutions, and the expansion of positivity for the class of mixed local-nonlocal superposition fractional operators.

C2weakest assumption

The structural assumptions on the mixed operator (kernel conditions, ellipticity constants, and the precise form of the superposition) are sufficient to carry the De Giorgi-Nash-Moser iteration through without additional restrictions on the sign or the support of the solution.

C3one line summary

Authors prove Caccioppoli inequalities, local boundedness, Hölder continuity, weak Harnack inequalities, and expansion of positivity for weak solutions of mixed fractional superposition operators.

References

46 extracted · 46 resolved · 0 Pith anchors

[1] D. G. Afonso, R. Bartolo, and G. M. Bisci. Multiple solutions to asymptotically linear problems driven by superposition operators.J. Math. Anal. Appl., 553(1):1–14, Article No. 129846, 2026 2026

[2] Y. Aikyn, S. Ghosh, V. Kumar, and M. Ruzhansky. Brezis-Nirenberg type problems associated with nonlinear superposition operators of mixed fractional order.arXiv preprint arXiv:2504.05105, pages 1–50, 2025

[3] Y. Aikyn, S. Ghosh, V. Kumar, and M. Ruzhansky. Spectral analysis, maximum principles and shape optimization for nonlinear superposition operators of mixed fractional order.arXiv preprint arXiv:2511.0 2025

[4] S. Bhowmick, S. Ghosh, and V. Kumar. Infinitely many solutions for nonlinear superposition operators of mixed fractional order involving critical exponent.Discrete Contin. Dyn. Syst.-S, pages 1–24, do 2026 · doi:10.3934/dcdss.2026089

[5] S. Bhowmick, S. Ghosh, and V. Kumar. Superlinear problems involving nonlinear superposi- tion operators of mixed fractional order.Proc. Roy. Soc. Edinburgh Sect. A, pages 1–26, doi– 10.1017/prm.2026.1 2026 · doi:10.1017/prm.2026.10124

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:53.663960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bf6037c6644456c276bd9f369d896aff7912aa59fd6f4f92ad1b01a1c81d2b6

Aliases

arxiv: 2605.15346 · arxiv_version: 2605.15346v1 · doi: 10.48550/arxiv.2605.15346 · pith_short_12: FP3AG7DGIRCW · pith_short_16: FP3AG7DGIRCWYJ3L · pith_short_8: FP3AG7DG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FP3AG7DGIRCWYJ3L3HZWTWEWV7 \
  | 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: 2bf6037c6644456c276bd9f369d896aff7912aa59fd6f4f92ad1b01a1c81d2b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07b585f4e27a72d068fc2958c09f8b6c2c042bd2bbd69b1a3a21e55fc308bdc5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-14T19:15:30Z",
    "title_canon_sha256": "20c53bff3fb67f4dbe609c9a2a22cbe7cc19468a384c675bbc94dfd9e7b35ee3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15346",
    "kind": "arxiv",
    "version": 1
  }
}