Pith Number

pith:HR2O3YK2

pith:2026:HR2O3YK2UT6S4UQT6I22VUJRY4

not attested not anchored not stored refs resolved

Spectral Properties of the Logarithmic Laplacian with Indefinite Weights

Arshi Vaishnavi, Rakesh Arora, Tuhina Mukherjee

The logarithmic Laplacian with indefinite weights has an unbounded sequence of Lusternik-Schnirelmann eigenvalues, only the first of which has a constant-sign eigenfunction.

arxiv:2605.13513 v1 · 2026-05-13 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HR2O3YK2UT6S4UQT6I22VUJRY4}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

We prove the existence of an unbounded sequence of Lusternik-Schnirelman eigenvalues and show that the first eigenvalue is simple, with the associated eigenfunction having constant sign in the domain. In contrast, eigenfunctions corresponding to higher eigenvalues necessarily change sign.

C2weakest assumption

The weight function is indefinite (changes sign) but belongs to a suitable function space such as L^infty(Omega), and the domain is bounded with sufficient regularity for the logarithmic Laplacian to be well-defined.

C3one line summary

Existence of an unbounded sequence of Lusternik-Schnirelmann eigenvalues is shown for the logarithmic Laplacian with indefinite weights; the first eigenvalue is simple with constant-sign eigenfunction, higher ones change sign, and nodal inequalities plus monotonicity hold.

References

46 extracted · 46 resolved · 0 Pith anchors

[1] Allegretto,Principal eigenvalues for indefinite-weight elliptic problems inR n, Proc 1992

[2] T. V. Anoop, M. Lucia and M. Ramaswamy,Eigenvalue problems with weights in Lorentz spaces, Calc. Var. Partial Differential Equations36(2009), no. 3, 355-376 2009

[3] R. Arora, J. Giacomoni and A. Vaishnavi,The Brezis-Nirenberg and logistic problem for the Logarithmic Laplacian, arXiv preprint arXiv:2504.18907 (2025) 2025

[4] R. Arora, J. Giacomoni, H. Hajaiej and A. Vaishnavi,Sharp embeddings and existence results for Logarithmicp-Laplacian equations with critical growth, accepted in NoDEA (2026), arXiv preprint arXiv:251 2026

[5] R. Arora, H. Hajaiej and K. Perera,Nonlocal Dirichlet problems involving the Logarithmic p-Laplacian, arXiv preprint arXiv:2512.21959 (2025) 2025

Receipt and verification

First computed	2026-05-18T02:44:24.532165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c74ede15aa4fd2e5213f235aad131c70b0043d9886ae203581ca0cd9ff17865

Aliases

arxiv: 2605.13513 · arxiv_version: 2605.13513v1 · doi: 10.48550/arxiv.2605.13513 · pith_short_12: HR2O3YK2UT6S · pith_short_16: HR2O3YK2UT6S4UQT · pith_short_8: HR2O3YK2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HR2O3YK2UT6S4UQT6I22VUJRY4 \
  | 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: 3c74ede15aa4fd2e5213f235aad131c70b0043d9886ae203581ca0cd9ff17865

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfc7a4e248f5c88bd05633bdc4d9fc6acd572dd54b32f1bd476137713419fa97",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T13:31:57Z",
    "title_canon_sha256": "5b9866db1dadcbf51af8a7b82dc165deb7e5514787808d5800409cd0a470eaf5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13513",
    "kind": "arxiv",
    "version": 1
  }
}