Pith Number

pith:X3EPP3ZI

pith:2026:X3EPP3ZIQQFJ5EXNSQGWGAVPNG

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A new proof of the transfer of regularity for kinetic equations

Lukas Niebel

A trajectory-based method proves transfer of regularity for kinetic equations at the weak scale of local diffusion.

arxiv:2605.13582 v1 · 2026-05-13 · math.AP

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Claims

C1strongest claim

We present a new trajectory-based approach to transfer-of-regularity estimates à la Bouchut-Hörmander for kinetic equations at the weak scale of local diffusion, yielding sharp, scale-invariant homogeneous estimates.

C2weakest assumption

The approach works at the weak scale of local diffusion for standard kinetic equations, with the abstract providing no further details on coefficient regularity or domain assumptions required for the trajectory method to close.

C3one line summary

A trajectory-based approach yields sharp, scale-invariant transfer-of-regularity estimates for kinetic equations at the local diffusion scale without Fourier computations or the fundamental solution.

References

28 extracted · 28 resolved · 0 Pith anchors

[1] Variational methods for the kinetic Fokker-Planck equation.Anal 1953

[2] Enhanced dissipation and H¨ ormander’s hypoellipticity.J 2022

[3] Fractional order kinetic equations and hypoellipticity.Anal 2012

[4] Poincar´ e inequality and quantitative De Giorgi method for hypoelliptic operators,

[5] Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness, 2024 2024

Formal links

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Cited by

1 paper in Pith

On the kinetic $p$-Laplace equation with nonlocal diffusion

Receipt and verification

First computed	2026-05-18T02:44:23.214805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bec8f7ef28840a9e92ed940d6302af69b7ae31b95fe22af69b77d10030366624

Aliases

arxiv: 2605.13582 · arxiv_version: 2605.13582v1 · doi: 10.48550/arxiv.2605.13582 · pith_short_12: X3EPP3ZIQQFJ · pith_short_16: X3EPP3ZIQQFJ5EXN · pith_short_8: X3EPP3ZI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/X3EPP3ZIQQFJ5EXNSQGWGAVPNG \
  | 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: bec8f7ef28840a9e92ed940d6302af69b7ae31b95fe22af69b77d10030366624

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "8b70ad9ede5cf3200147adaa2336efc82639b811fd752b54e3f4ac8b48676210",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T14:15:24Z",
    "title_canon_sha256": "5ad3d3034c4b0cfefb9713ff31f5eb532360e534459612d9f395156eebd41f1b"
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    "kind": "arxiv",
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