Pith Number

pith:NA2NWNPL

pith:2026:NA2NWNPLTSL7WPBL6PVSFHKFIE

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Lax-Oleinik formula for nonautonomous Hamilton-Jacobi equations on networks

Marco Pozza

A Lax-Oleinik-type representation formula yields the unique solution to nonautonomous Hamilton-Jacobi equations on networks with loops and countably many arcs.

arxiv:2605.13704 v1 · 2026-05-13 · math.AP

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Claims

C1strongest claim

We provide a Lax-Oleinik-type representation formula for solutions to nonautonomous Hamilton-Jacobi equations posed on networks with a rather general geometry. [...] the formula yields the unique solution to the problem even when the flux limiters exceed standard upper bounds.

C2weakest assumption

The Hamiltonians are convex and superlinear in the momentum variable and satisfy a Lipschitz-type condition in the time variable; the networks may possess countably many arcs and allow loops, with flux limiters at vertices ensuring well-posedness.

C3one line summary

A Lax-Oleinik representation formula is established for nonautonomous Hamilton-Jacobi equations on general networks, yielding unique solutions via an action functional whose minimizers are Lipschitz continuous without excluding the Zeno phenomenon.

References

25 extracted · 25 resolved · 0 Pith anchors

[1] Deterministic mean field games on networks: a Lagrangian approach 2024 · doi:10.1137/23m1615073

[2] M. Bardi and I. Capuzzo-Dolcetta.Optimal control and viscosity solutions of Hamilton- Jacobi-Bellman equations. Birkhäuser Boston, 1997.isbn: 978-0-8176-4755-1.doi:10.1007/ 978-0-8176-4755-1 1997

[3] Existence ofC1,1 critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds 2007 · doi:10.1016/j.ansens.2007.01.004

[4] 2001 , PAGES = 2001 · doi:10.1090/gsm/033

[5] Error estimate for a semi-Lagrangian scheme for Hamilton-Jacobi equations on networks 2025 · doi:10.1007/s42967-025-00527-w

Formal links

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Receipt and verification

First computed	2026-05-18T02:44:16.822045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6834db35eb9c97fb3c2bf3eb229d45413f864ef1b85f59831c15f8633bbc6472

Aliases

arxiv: 2605.13704 · arxiv_version: 2605.13704v1 · doi: 10.48550/arxiv.2605.13704 · pith_short_12: NA2NWNPLTSL7 · pith_short_16: NA2NWNPLTSL7WPBL · pith_short_8: NA2NWNPL

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NA2NWNPLTSL7WPBL6PVSFHKFIE \
  | 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: 6834db35eb9c97fb3c2bf3eb229d45413f864ef1b85f59831c15f8633bbc6472

Canonical record JSON

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    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T15:53:14Z",
    "title_canon_sha256": "b2e9e1f0aa9c0171381aa63482a50810f71a69e8668406749d2bfcc437aa7ac0"
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