Pith Number

pith:O7SV2NKC

pith:2026:O7SV2NKCZX74K2GUU2YAZEFILA

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Classification of solutions to the singular Liouville's equation associated with the $N$ Finsler Laplacian

Jianwei Xue, Maochun Zhu

Solutions to the singular Finsler-N-Laplacian Liouville equation are fully classified when the total mass is finite.

arxiv:2605.13447 v1 · 2026-05-13 · math.AP · math.FA

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Claims

C1strongest claim

We classify a class of singular Liouville's equation associated with the Finsler-N-Laplacian for any β∈(0,N) under the finite mass condition ∫ R^N hat F^o(x)^{-β} e^u dx < +∞, relaxing the mass condition required in the classification result in [39].

C2weakest assumption

The finite mass condition holds and F is convex and positively homogeneous of degree 1, allowing the Finsler structure to support the divergence-form operator and the classification analysis.

C3one line summary

Solutions to the singular Liouville equation associated with the Finsler-N-Laplacian are classified under a relaxed finite mass condition.

References

55 extracted · 55 resolved · 1 Pith anchors

[1] Druet, Blow-up analysis in dimension 2 and a sharp form of Trudinger–Moser in- equality, Commun 2004

[2] J.A. Aguilar Crespo, I.P. Alonso, Blow-up behavior for solutions of−∆ N u=V(x)e u in bounded domains inR N, Nonlinear Anal. 29 (1997) 365-384 1997

[3] M. Belloni, V. Ferone, B. Kawohl, Isoperimetric inequalities, wulffshape and related questions for strongly nonlinear elliptic operators, Z. Angew. Math. Phys. 54 (2003) 771-783 2003

[4] E. Berchio, A. Ferrero, D. Ganguly, P. Roychowdhury, Classification of radial solutions to−∆gu=e u on Riemannian models, J. Differ. Equations 361 (2023) 417–448 2023

[5] C. Bianchini, G. Ciraolo, Wulff shape characterizations in overdetermined anisotropic elliptic prob- lems, Comm. Partial Differential Equations. 43 (2018) 790-820 2018

Receipt and verification

First computed	2026-05-18T02:44:41.940151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77e55d3542cdffc568d4a6b00c90a858351a86594b4a9f7ffd20e2c036520cf5

Aliases

arxiv: 2605.13447 · arxiv_version: 2605.13447v1 · doi: 10.48550/arxiv.2605.13447 · pith_short_12: O7SV2NKCZX74 · pith_short_16: O7SV2NKCZX74K2GU · pith_short_8: O7SV2NKC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/O7SV2NKCZX74K2GUU2YAZEFILA \
  | 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: 77e55d3542cdffc568d4a6b00c90a858351a86594b4a9f7ffd20e2c036520cf5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4125f87173b5c00fe74cd4d19494de4724441f4b041d383e4dc0f039d917a74e",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T12:42:41Z",
    "title_canon_sha256": "445a71dbed2498cd41b3d0c23fbb2af1ff6547889c5df7e0f94f546949718666"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13447",
    "kind": "arxiv",
    "version": 1
  }
}