Pith Number

pith:RLB7WQPK

pith:2026:RLB7WQPKMETKF3GNUNHXXJ3FAM

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The Dirichlet problem for double divergence form elliptic equations with measures as boundary conditions

S.V. Shaposhnikov, V.I. Bogachev

Solvability established for Dirichlet problems on double divergence elliptic equations with measure boundary conditions

arxiv:2604.17096 v2 · 2026-04-18 · math.AP

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\pithnumber{RLB7WQPKMETKF3GNUNHXXJ3FAM}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

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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 broad assumptions we establish the solvability of this problem. It is also shown that a solution to a double divergence form equation on a domain serves as a solution to the Dirichlet problem on inner subdomains.

C2weakest assumption

The 'broad assumptions' on the low-regularity coefficients and the general Borel measures as boundary data, which are not specified in the abstract and whose precise form is required for the solvability claim.

C3one line summary

Solvability is established for the Dirichlet problem for double divergence form elliptic equations with measure boundary data under broad assumptions on coefficients.

Receipt and verification

First computed	2026-05-26T02:04:10.949857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ac3fb41ea6126a2eccda34f7ba765032e1bbb0f4a7072032e1e6ef7db219ce3

Aliases

arxiv: 2604.17096 · arxiv_version: 2604.17096v2 · doi: 10.48550/arxiv.2604.17096 · pith_short_12: RLB7WQPKMETK · pith_short_16: RLB7WQPKMETKF3GN · pith_short_8: RLB7WQPK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RLB7WQPKMETKF3GNUNHXXJ3FAM \
  | 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: 8ac3fb41ea6126a2eccda34f7ba765032e1bbb0f4a7072032e1e6ef7db219ce3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1be1fad1ffbaaf92dc84a102eef9d9879e37300b708e0411b9db3932cd515fe6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-04-18T18:17:54Z",
    "title_canon_sha256": "81809cc9ecfd3e3f1265451ab554b920fdba9b825f86ee71edf929face0e23b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.17096",
    "kind": "arxiv",
    "version": 2
  }
}