Pith Number

pith:EQTPOZDT

pith:2026:EQTPOZDT34TXR7ZDNOMDGGIPCI

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Schauder estimates and classical solutions of the Dirichlet problem for stochastic parabolic equations

Kai Du

A compatibility condition on gradient noise allows global Schauder estimates in stochastic Hölder spaces for stochastic parabolic Dirichlet problems.

arxiv:2604.17973 v2 · 2026-04-20 · math.PR

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Claims

C1strongest claim

Under a natural compatibility condition on the gradient noise, we establish global Schauder estimates in stochastic Hölder spaces for the Dirichlet problem. As a consequence, we obtain existence and uniqueness of quasi-classical solutions in stochastic Hölder spaces, and further derive pathwise classical solvability in Hölder classes.

C2weakest assumption

The natural compatibility condition on the gradient noise together with the assumption that coefficients are Hölder continuous in space while only their boundary traces are Hölder continuous in time.

C3one line summary

Global Schauder estimates and existence of quasi-classical and pathwise classical solutions are proved for the Dirichlet problem of stochastic parabolic equations in stochastic Hölder spaces.

Receipt and verification

First computed	2026-05-20T00:04:31.998464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2426f76473df2778ff236b9833190f1216c7a16a5d7f855f804529b5de6c5bda

Aliases

arxiv: 2604.17973 · arxiv_version: 2604.17973v2 · doi: 10.48550/arxiv.2604.17973 · pith_short_12: EQTPOZDT34TX · pith_short_16: EQTPOZDT34TXR7ZD · pith_short_8: EQTPOZDT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EQTPOZDT34TXR7ZDNOMDGGIPCI \
  | 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: 2426f76473df2778ff236b9833190f1216c7a16a5d7f855f804529b5de6c5bda

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "c316f0ba2cc307cf9079ee0639f5b7b54d8a18b6e0884fe0941f193a5b2cd0d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-20T08:52:26Z",
    "title_canon_sha256": "09e4a5900e3aa9ad7a1168babec5d34b39e641cc9d390f4112f3d8ddc0d4b62f"
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  "source": {
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    "kind": "arxiv",
    "version": 2
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}