Pith Number

pith:PC4HXAJ3

pith:2026:PC4HXAJ3FUMME62OS7KAYNFBZM

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Dirichlet Green's functions with singular drifts at the boundary of convex domains

Aritro Pathak

Dirichlet Green's functions for Laplacian-plus-drift operators satisfy interior pointwise upper bounds in convex domains.

arxiv:2604.10622 v2 · 2026-04-12 · math.AP

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\pithnumber{PC4HXAJ3FUMME62OS7KAYNFBZM}

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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

In convex bounded domains in R^n with n >= 3, we establish interior pointwise upper bounds for the Dirichlet Green's function of elliptic operators ... whose principal part is the Laplacian and which include a drift term that diverges near the boundary like a negative power of the distance with exponent strictly less than 1.

C2weakest assumption

The domain must be convex and bounded, the drift singularity exponent must be strictly less than 1, and the operator must have Laplacian principal part; if convexity fails or the exponent reaches 1, the interior bounds may cease to hold.

C3one line summary

Interior pointwise upper bounds are established for Dirichlet Green's functions of Laplacian-plus-singular-drift elliptic operators in convex bounded domains in R^n for n greater than or equal to 3.

Receipt and verification

First computed	2026-06-23T02:12:48.973472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78b87b813b2d18c27b4e97d40c34a1cb230efbf863e820f1ce0b6086c82dfd90

Aliases

arxiv: 2604.10622 · arxiv_version: 2604.10622v2 · doi: 10.48550/arxiv.2604.10622 · pith_short_12: PC4HXAJ3FUMM · pith_short_16: PC4HXAJ3FUMME62O · pith_short_8: PC4HXAJ3

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PC4HXAJ3FUMME62OS7KAYNFBZM \
  | 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: 78b87b813b2d18c27b4e97d40c34a1cb230efbf863e820f1ce0b6086c82dfd90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce2fb1a98802884ce42f3ebad77eaef450fe734c1140ce1c0207db0abdfe10ed",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-04-12T12:58:33Z",
    "title_canon_sha256": "477ac3d8c6b1ce6b76ed634d9e5703d26e58d960d492ed40f73c5af8d4d0f182"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.10622",
    "kind": "arxiv",
    "version": 2
  }
}